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Solutions are categorized in 16 chapters, each chapter is a .doc format.
NOTE: Multiple Exams and Quizzes from last quarters are included.
Introduction to Management Science, 10e (Taylor)
Chapter 1 Management Science
1) Management science involves the philosophy of approaching a problem in a subjective manner.
2) Management science techniques can be applied only to business and military organizations.
3) Once management scientist makes his or her decision and recommendation to management, then typically, his or her involvement with the problem is finished.
4) A variable is a value that is usually a coefficient of a parameter in an equation.
5) Parameters are known, constant values that are usually coefficients of variables in equations.
6) Data are pieces of information from the problem environment.
7) A model is a mathematical representation of a problem situation including variables, parameters, and equations.
8) A management science technique usually applies to a specific model type.
9) The first step of the management science process is to define the problem.
10) Management science modeling techniques provide results that are known with certainty.
11) The term sensitivity analysis refers to testing how a problem solution reacts to changes in one or more of the model parameters.
12) Fixed costs depend on the number of items produced.
13) Variable costs depend on the number of items produced.
14) Fixed cost is the difference between total cost and total variable cost.
15) The break-even point is the volume that equates total revenue with total cost.
16) In general, an increase in price increases the break even point if all costs are held constant.
17) If variable costs increase, but price and fixed costs are held constant, the break even point will decrease.
18) Managers utilize spreadsheets to conduct their own analyses in management science studies.
19) Management science techniques focus primarily on observation, model construction and implementation to find an appropriate solution to a problem.
20) Management science modeling techniques focus on model construction and problem solution.
21) Decision Support Systems (DSS) use computers to help decision makers address complex problems.
22) Enterprise Resource Planning (ERP) system is a data oriented decision support system that utilizes specific management science solution procedures to solve individual problems such as cost-volume analysis.
23) A __________ is a symbol used to represent an item that can take on any value.
24) __________ are known, constant values that are coefficients of variables in equations.
25) __________ are pieces of information from the problem environment.
26) A __________ is a functional relationship including variables, parameters, and equations.
27) Management science techniques include __________ techniques, models that are represented as diagrams, presenting a pictorial representation of the system being analyzed.
28) __________ techniques provide results that contain uncertainty, unlike mathematical programming techniques which are deterministic.
29) __________ costs are independent of the volume of goods produced and remain constant.
30) __________ depend on the number of items produced.
31) Total revenue minus total cost equals __________ .
32) The __________ is the volume that equates total revenue with total cost.
33) A __________ represents a limitation to achieving maximum profits due to limited resources.
34) A __________ programming technique refers to a predetermined set of mathematical steps used to solve a problem.
35) A __________ is a computer-based system that helps decision-makers address complex problems that involve different parts of an organization and operations.
36) The relationship d = 5000 – 25p describes what happens to demand (d) as price (p) varies. Price can vary between \$10 and \$50. How many units can be sold when the price is \$10?
37) The supplier of cans for Coors Brewery, Valley Metal Container, uses a __________ to determine the weekly production schedule for cans in order to meet brewery demand.
38) A production process requires a fixed cost of \$50,000. The variable cost per unit is \$25 and the revenue per unit is projected to be \$45. Write a mathematical expression for total cost.
39) A production process requires a fixed cost of \$50,000. The variable cost per unit is \$25 and the revenue per unit is projected to be \$45. Write a mathematical expression for total revenue.
40) A production process requires a fixed cost of \$50,000. The variable cost per unit is \$25 and the revenue per unit is projected to be \$45. Write a mathematical expression for total profit.
41) A production process requires a fixed cost of \$50,000. The variable cost per unit is \$25 and the revenue per unit is projected to be \$45. Find the break-even point.
42) A production process requires a fixed cost of \$50,000 and the variable cost per unit is \$25. The revenue per unit was projected to be \$45 but a recent marketing study shows that because of an emerging competitor, the revenue will be about 12% lower. How does this affect the break even point?
43) Administrators at a university will charge students \$150 to attend a seminar. It costs \$3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs \$25 per student for the administrators to provide the course materials. How many students would have to register for the seminar for the university to break even?
44) Administrators at a university are planning to offer a summer seminar. It costs \$3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs \$25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even?
45) Administrators at a university are planning to offer a summer seminar. It costs \$3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs \$25 per student for the administrators to provide the course materials. If 30 students attend the seminar, how much of a profit (or loss) will be incurred?
46) A newly opened bed-and-breakfast projects the following:
Monthly fixed costs \$8000
Variable cost per occupied room per night \$40
Revenue per occupied room per night \$165
Write the expression for total cost per month.
47) A newly opened bed-and-breakfast projects the following:
Monthly fixed costs \$8000
Variable cost per occupied room per night \$40
Revenue per occupied room per night \$165
Write the expression for total revenue per month.
48) A newly opened bed-and-breakfast projects the following:
Monthly fixed costs \$8000
Variable cost per occupied room per night \$40
Revenue per occupied room per night \$165
How many rooms would have to be occupied per month in order to break even?
49) A script writer has received an advance against royalties of \$10000. The royalty rate is \$2 for every performance in the US, and \$3 for every performance outside the US. Define variables for this problem.
50) A script writer has received an advance against royalties of \$10,000. The royalty rate is \$2 for every performance in the US, and \$3 for every performance outside the US. Write an expression that could be used to compute the number of performances in order to cover the advance.
51) Students are organizing a “Battle of the Bands” contest. They know that at least 100 people will attend. The rental fee for the hall is \$150 and the winning band will receive \$500. In order to guarantee that they break even, how much should they charge for each ticket?
52) A manufacturer buys peas for vegetable pies from 2 cooperatives. The price per unit is \$6 from cooperative A, and \$5.50 per unit from cooperative B. Define variables that would tell how many units to purchase from each source.
53) A manufacturer buys peas for vegetable pies from 2 cooperatives. The price per unit is \$6 from cooperative A, and \$5.50 per unit from cooperative B. Develop an objective function that would minimize the total cost.
54) A manufacturer buys peas for vegetable pies from 2 cooperatives. The price per unit is \$6 from cooperative A, and \$5.50 per unit from cooperative B. The manufacturer needs at least 12000 units of peas. Cooperative A can supply up to 8000 units, and cooperative B can supply at least 6000 units. Develop constraints for these conditions.
55) A manager of the cereal bar at the college campus has determined that the profit made for each bowl of Morning Buzz cereal sold, x, is equal to: Z = \$4x – 0.5x. Each bowl of Morning Buzz weighs 6 ounces, and the manager has 12 lbs (192 ounces) of cereal available each day, which can be written as the constraint, 6x ≤192. How much profit will be made from Morning Buzz if it is all sold in one day?
56) The College Coffee Café buys tea from 3 suppliers. The price per pound is \$15.00 from supplier A, \$17.50 from supplier B, and \$21.00 from supplier C. They have budged \$175 to purchase the tea. The café needs at least 12 pounds of tea, and supplier C can supply no more than 4 pounds. Develop constraints for these conditions.
57) The College Coffee Café receives a profit of \$1.25 for each cup of house tea that they sell, \$1.40 for each cup of the premium brand, and \$1.50 for each cup of their special blend that they sell. Develop an objective that maximizes profit.
58) The steps of the management science process are:
A) problem definition, model construction, observation, model solution, implementation.
B) observation, problem definition, model construction, model solution, implementation.
C) model construction, problem definition, observation, model solution, implementation.
D) observation, implementation, problem definition, model construction, model solution.
59) A model is a functional relationship that includes:
A) variables
B) parameters
C) equations
D) all of the above
60) Which of the following is an equation or an inequality that expresses a resource restriction in a mathematical model?
A) a decision variable.
B) data
C) an objective function.
D) a constraint.
E) a parameter.
61) Which of the following is incorrect with respect to the use of models in decision making?
A) they improve understanding of the problem
B) they promote subjectivity in decision making
C) they are generally easy to use
D) they provide a systematic approach to problem solving
62) The field of management science
A) approaches decision making rationally with techniques based on the scientific method
B) is another name for decision science and for operations research
C) concentrates on the use of quantitative methods to assist managers in decision making
D) all of the above
63) The processes of problem observation
A) cannot be done until alternatives are proposed
B) requires consideration of multiple criteria
C) is the first step of decision making
D) is the final step of problem solving
64) The limits of the problem and the degree to which it pervades other units in the organization must be included during the __________ step of the management science process.
A) observation
B) definition
C) solution
D) implementation
65) __________ involves determining the functional relationship between variables, parameters and equations
A) Problem observation
B) Problem definition
C) Model construction
D) Model solution
E) Model implementation
66) Which steps of the management science process can either be a recommended decision or information that helps a manager make a decision?
A) model implementation
B) model construction
C) problem definition
D) model solution
E) problem formulation
67) The quantitative analysis approach requires
A) mathematical expressions for the relationship
B) uncomplicated problems
C) the manager to have prior experience with similar problems
D) all of the above
68) The result of an effective decision making process should be monitored in order to
A) reveal wrong assumptions
B) reveal errors in the implementation
C) insure the achievement of desired results
D) all of the above
69) The management science process does not include
A) problem definition
B) feedback
C) implementation
D) subjective preference
E) information
70) The indicator that results in total revenues being equal to total cost is called the
A) marginal cost
B) marginal volume
C) break-even point
D) profit mix
71) Variable cost
A) depends on the number of units produced
B) plus marginal cost equals fixed cost
C) is equal to total cost in deterministic models
D) is the same as average cost
72) The components of break-even analysis are
A) cost and profit
B) volume and cost
C) volume, cost and profit
D) volume and profit
73) __________ are generally independent of the volume of units produced and sold.
A) Fixed costs
B) Variable costs
C) Profits
D) average cost
74) The purpose of break-even analysis is to determine the number of units of a product to sell that will
A) appeal to the consumer
B) result in a profit
C) result in a loss
D) result in zero profit
75) Variable cost does not include
A) raw materials and resources
B) staff and management salaries
C) material handling and freight
D) direct labor and packaging
76) Which variable is not a component of break-even analysis?
A) fixed costs
B) variable costs
C) number of employees
D) total costs
E) number of customers
77) At the break-even point
A) total revenue equals total cost
B) profit is maximized
C) revenue is maximized
D) costs are minimized
78) If the price increases but fixed and variable costs do not change, the break even point
A) decreases
B) increases
C) remains the same
D) may increase or decrease, depending on sales
79) If the price decreases but fixed and variable costs do not change, the break even point
A) decreases
B) increases
C) remains the same
D) may increase or decrease, depending on sales
80) The term __________ refers to testing how a problem solution reacts to changes in one or more of the model parameters.
A) graphical solution
B) decision analysis
C) decision science
D) sensitivity analysis
E) break-even analysis
81) If fixed costs decrease, but variable cost and price remain the same, the break even point
A) decreases
B) increases
C) remains the same
D) may increase or decrease depending on sales
82) If fixed costs increase, but variable cost and price remain the same, the break even point
A) decreases
B) increases
C) remains the same
D) may increase or decrease depending on sales
83) EKA manufacturing company produces Part # 2206 for the aerospace industry. Each unit of part # 2206 is sold for \$15. The unit production cost of part # 2206 is \$3. The fixed monthly cost of operating the production facility is \$3000. How many units of part # 2206 have to be sold in a month to break-even?
A) 166.67
B) 200
C) 250
D) 500
E) 1000
84) EKA manufacturing company produces Part # 2206 for the aerospace industry. The unit production cost of part # 2206 is \$3. The fixed monthly cost of operating the production facility is \$3000. Next month’s demand for part # 2206 is 200 units. How much should the company charge for each unit of part # 2206 to break-even?
A) 10
B) 12
C) 15
D) 18
E) 20
85) A bed and breakfast even every month if they book 30 rooms over the course of a month. Their fixed cost is \$6000 per month and the revenue they receive from each booked room is \$180. What their variable cost per occupied room?
A) \$30
B) \$40
C) \$48
D) \$62
86) Administrators at a university will charge students \$150 to attend a seminar. It costs \$3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs \$25 per student for the administrators to provide the course materials. How many students would have to register for the seminar for the university to break even?
A) 16
B) 18
C) 20
D) 24
E) 30
87) A university is planning a seminar. It costs \$3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs \$25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even?
A) 100
B) 120
C) 150
D) 175
E) 200
88) It costs \$50,000 to start a production process. Variable cost is \$25 per unit and revenue is \$\$45 per unit. What is the break even point?
A) 1000 units
B) 1111 units
C) 2000 units
D) 2500 units
89) Which of the following statements is false?
A) Decision models selectively describe the managerial situation.
B) Decision models consider all factors from the real world.
C) Decision models designate performance measures that reflect objectives.
D) Decision models designate decision variables.
90) A difficult aspect of using spreadsheets to solve management science problems is
A) obtaining the solution to standard management science problems
B) data entry
C) performing sensitivity analysis
D) setting up a spreadsheet with complex models and formulas
91) A technique that assumes certainty in its solution is referred to as
A) indeterminate
B) probabilistic
C) deterministic
D) parametric
92) Classification of management science techniques does not recognize
A) linear mathematical programming
B) probabilistic techniques
C) network techniques
D) computer programming
93) Linear mathematical programming techniques assume that all parameters in the models are
A) known with certainty
B) unknown
C) predictable
D) unpredictable
94) Decision analysis is a __________ technique.
A) linear mathematical programming
B) probabilistic
C) network
D) simulation
E) non-linear programming technique
95) Which one of the following techniques is not a mathematical programming technique?
A) linear programming models
B) transportation models
C) analytical hierarchy process
D) goal programming
E) integer linear programming technique
96) Which one of the following management science methods is not a probabilistic technique?
A) assignment models
B) decision analysis
C) queuing analysis
D) statistical analysis
97) A baker uses organic flour from a local farmer in all of his baked goods. For each batch of bread (x1), he uses 4 lbs. For a batch of cookies (x2), he uses 3 pounds, and for a batch of muffins (x3) he uses 2 pounds. The local farmer can supply him with no more than 24 pounds per week. The constraint that represents this condition is:
A) x1 ≤ 8, x2 ≤ 8, x3 ≤ 8
B) x1+ x2 + x3 ≥ 24
C) x1 ≤ 6, x2 ≤ 8, x3 ≤ 12
D) x1+ x2 + x3 ≤ 24
E) 4×1+ 3×2 + 2×3 ≤ 24
98) An objective function
A) is a part of a model
B) represents the objective of the firm
C) can represent costs or profits
D) A and B only
E) all of the above
99) Larry’s Fish Market buys salmon (S) for \$5 per pound and a local whitefish (W) for \$3.50 per pound. Larry wants to minimize his cost, but he cannot spend more than \$160. The objective function that minimizes these costs for Larry is:
A) 5S + 3.5W = 160
B) 5S + 3.5W ≤ 160
C) Min 5S + 3.5 W
D) Max 5S + 3.5 W
E) 5S + 3.5W ≥ 160
100) Taco Bell used which of the following management science techniques to help save over \$53 million?
A) linear programming and network analysis
B) forecasting, queuing theory and inventory analysis
C) goal programming and network analysis
D) forecasting, simulation and integer programming
Introduction to Management Science, 10e (Taylor)
Chapter 2 Linear Programming: Model Formulation and Graphical Solution

1) Linear programming is a model consisting of linear relationships representing a firm’s decisions given an objective and resource constraints.
2) The objective function is a linear relationship reflecting the objective of an operation.
3) A constraint is a linear relationship representing a restriction on decision making.
4) A linear programming model consists of only decision variables and constraints.
5) A feasible solution violates at least one of the constraints.
6) Proportionality means the slope of a constraint is proportional to the slope of the objective function.
7) The terms in the objective function or constraints are additive.
8) The terms in the objective function or constraints are multiplicative.
9) The values of decision variables are continuous or divisible.
10) All model parameters are assumed to be known with certainty.
11) In linear programming models , objective functions can only be maximized.
12) All linear programming models exhibit a set of constraints.
13) Linear programming models exhibit linearity among all constraint relationships and the objective function.
14) The equation 8xy = 32 satisfies the proportionality property of linear programming.
15) Objective functions in linear programs always minimize costs.
16) The feasible solution area contains infinite solutions to the linear program.
17) There is exactly one optimal solution point to a linear program.
18) The following equation represents a resource constraint for a maximization problem: X + Y ≥ 20
19) A minimization model of a linear program contains only surplus variables.
20) In the graphical approach, simultaneous equations may be used to solve for the optimal solution point.
21) Slack variables are only associated with maximization problems.
22) Surplus variables are only associated with minimization problems.
23) If the objective function is parallel to a constraint, the constraint is infeasible.
24) Multiple optimal solutions occur when constraints are parallel to each other.
25) Graphical solutions to linear programming problems have an infinite number of possible objective function lines.
26) The first step in formulating a linear programming model is to define the objective function.
27) __________ are mathematical symbols representing levels of activity.
28) The __________ is a linear relationship reflecting the objective of an operation.
29) A __________ is a linear relationship representing a restriction on decision making.
30) If at least one constraint in a linear programming model is violated the solution is said to be __________.
31) A graphical solution is limited to solving linear programming problems with __________ decision variables
32) The __________ solution area is an area bounded by the constraint equations.
33) Multiple optimal solutions can occur when the objective function line is __________ to a constraint line.
34) When a maximization problem is __________, the objective function can increase indefinitely without reaching a maximum value.
35) A linear programming problem that results in a solution that is __________ usually indicates that the linear program has been incorrectly formulated.
Diff: 2 Page Ref: 54
Main Heading: Graphical Solutions of Linear Programming Models
Key words: graphical solution, infeasible solution
36) In a constraint the __________ variable represents unused resources.
37) If the objective function is parallel to a constraint, the linear program could have __________.
38) Corner points on the boundary of the feasible solution area are called __________ points.
39) The __________ step in formulating a linear programming model is to define the decision variables.
40) The __________ property of linear programming models indicates that the values of all the model parameters are known and are assumed to be constant.
41) The __________ property of linear programming models indicates that the rate of change or slope of the objective function or a constraint is constant.
42) The __________ property of linear programming models indicates that the decision variables cannot be restricted to integer values and can take on any fractional value.
43) The constraint, 2X +XY violates the __________ property of linear programming.
44) Consider the following minimization problem:
Min z = x1 + 2×2
s.t. x1 + x2 ≥ 300
2×1 + x2 ≥ 400
2×1 + 5×2 ≤ 750
x1, x2 ≥ 0
What is the optimal solution?
45) Consider the following minimization problem:
Min z = x1 + 2×2
s.t. x1 + x2 ≥ 300
2×1 + x2 ≥ 400
2×1 + 5×2 ≤ 750
x1, x2 ≥ 0
Which constraints are binding at the optimal solution? (x1 =250, x2 = 50)
46) Solve the following graphically
Max z = 3×1 +4×2
s.t. x1 + 2×2 ≤ 16
2×1 + 3×2 ≤ 18
x1 ≥ 2
x2 ≤ 10
x1, x2 ≥ 0
What are the optimal values of x1, x2, and z?
47) Consider the following linear program:
MAX Z = 60A + 50B
s.t. 10A + 20B ≤ 200
8A + 5B ≤ 80
A ≥ 2
B ≥ 5
Solve this linear program graphically and determine the optimal quantities of A, B, and the value of Z.
48) Consider the following linear program:
MIN Z = 60A + 50B
s.t. 10A + 20B ≤ 200
8A + 5B ≤ 80
A ≥ 2
B ≥ 5
Solve this linear program graphically and determine the optimal quantities of A, B, and the value of Z.
49) A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function.
If this is a maximization, which extreme point is the optimal solution?
50) A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function.
If this is a minimization, which extreme point is the optimal solution?
51) A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function.
What would the be the new slope of the objective function if multiple optimal solutions occurred along line segment AB?
52) Consider the following linear programming problem:
Max Z = \$15x + \$20y
Subject to: 8x + 5y ≤ 40
0.4x + y ≥ 4
x, y ≥ 0
Determine the values for x and y that will maximize revenue. Given this optimal revenue, what is the amount of slack associated with the first constraint?
53) Max Z = \$3x + \$9y
Subject to: 20x + 32y ≤ 1600
4x + 2y ≤ 240
y ≤ 40
x, y ≥ 0
Solve for the quantities of x and y which will maximize Z. What is the value of the slack variable associated with constraint 2?
54) Max Z = 5×1 + 3×2
Subject to: 6×1 + 2×2 ≤ 18
15×1 + 20×2 ≤ 60
x1 , x2 ≥ 0
Find the optimal profit and the values of x1 and x2 at the optimal solution.
55) Max Z = 3×1 + 3×2
Subject to: 10×1 + 4×2 ≤ 60
25×1 + 50×2 ≤ 200
x1 , x2 ≥ 0
Find the optimal profit and the values of x1 and x2 at the optimal solution.
56) Consider the following linear programming problem:
MIN Z = 10×1 + 20×2
Subject to: x1 + x2 ≥ 12
2×1 + 5×2 ≥ 40
x2 ≥ 13
x1 , x2 ≥ 0
What is minimum cost and the value of x1 and x2 at the optimal solution?
57) Consider the following linear programming problem:
MIN Z = 10×1 + 20×2
Subject to: x1 + x2 ≥ 12
2×1 + 5×2 ≥ 40
x2 ≥ 13
x1 , x2 ≥ 0
At the optimal solution, what is the value of surplus and slack associated with constraint 1 and constraint 3 respectively?
58) Consider the following linear programming problem:
MIN Z = 2×1 + 3×2
Subject to: x1 + 2×2 ≤ 20
5×1 + x2 ≤ 40
4×1 +6×2 ≤ 60
x1 , x2 ≥ 0
What is the optimal solution?
59) A company producing a standard line and a deluxe line of dishwashers has the following time requirements (in minutes) in departments where either model can be processed.
Standard Deluxe
Stamping 3 6
Motor installation 10 10
Wiring 10 15
The standard models contribute \$20 each and the deluxe \$30 each to profits. Because the company produces other items that share resources used to make the dishwashers, the stamping machine is available only 30 minutes per hour, on average. The motor installation production line has 60 minutes available each hour. There are two lines for wiring, so the time availability is 90 minutes per hour.
Let x = number of standard dishwashers produced per hour
y = number of deluxe dishwashers produced per hour
Write the formulation for this linear program:
60) In a linear programming problem, the binding constraints for the optimal solution are:
5×1 + 3×2 ≤ 30
2×1 + 5×2 ≤ 20
As long as the slope of the objective function stays between __________ and __________, the current optimal solution point will remain optimal.
61) In a linear programming problem, the binding constraints for the optimal solution are:
5×1 + 3×2 ≤ 30
2×1 + 5×2 ≤ 20
Which of these objective functions will lead to the same optimal solution?
a. 2×1 + 1×2
b. 7×1 + 8×2
c. 80×1 + 60×2
d. 25×1 + 15×2
62) Decision variables
A) measure the objective function
B) measure how much or how many items to produce, purchase, hire, etc.
C) always exist for each constraint
D) measure the values of each constraint
63) In a linear programming problem, a valid objective function can be represented as
A) Max Z = 5xy
B) Max Z 5×2 + 2y2
C) Max 3x + 3y + 1/3z
D) Min (x1 + x2) / x3
64) Which of the following could not be a linear programming problem constraint?
A) 1A + 2B ≠ 3
B) 1A + 2B = 3
C) 1A + 2B ≤ 3
D) 1A + 2B ≥ 3
65) A linear programming model consists of
A) decision variables
B) an objective function
C) constraints
D) all of the above
66) The minimization of cost or maximization of profit is the
B) constraint of operations management
C) goal of management science
D) objective of linear programming
E) both A and D
67) Which of the following could be a linear programming objective function?
A) Z = 1A + 2BC + 3D
B) Z = 1A + 2B + 3C + 4D
C) Z = 1A + 2B / C + 3D
D) Z = 1A + 2B2 + 3D
E) all of the above
68) The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular (R) and diet (D). Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are \$3.00 per case and profits for diet soft drink are \$2.00 per case. What is the objective function?
A) MAX \$2R + \$4D
B) MAX \$3R + \$2D
C) MAX \$3D + \$2R
D) MAX \$4D + \$2R
E) MAX \$4R + \$2D
69) The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular (R) and diet(D). Two of the limited resources are production time (8 hours = 480 minutes per day) and syrup limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are \$3.00 per case and profits for diet soft drink are \$2.00 per case. What is the time constraint?
A) 2R + 5D ≤ 480
B) 2D + 4R ≤ 480
C) 2R + 3D ≤ 480
D) 3R + 2D ≤ 480
E) 2R + 4D ≤ 480
70) Non-negativity constraints
A) restrict the decision variables to zero.
B) restrict the decision variables to positive values
C) restrict the decision variables to negative values
D) do not restrict the sign of the decision variable.
E) both A and B
71) Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs \$500 and requires 100 cubic feet of storage space, and each medium shelf costs \$300 and requires 90 cubic feet of storage space. The company has \$75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is \$300 and for each medium shelf is \$150. What is the objective function?
A) MAX Z = \$300B + \$100 M
B) MAX Z = \$300M + \$150 B
C) MAX Z = \$300B + \$150 M
D) MAX Z = \$300B + \$500 M
E) MAX Z = \$500B + \$300 M
72) Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs \$500 and requires 100 cubic feet of storage space, and each medium shelf costs \$300 and requires 90 cubic feet of storage space. The company has \$75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is \$300 and for each medium shelf is \$150. What is the storage space constraint?
A) 90B + 100M ≥ 18000
B) 90B + 100M ≤ 18000
C) 100B + 90M ≤ 18000
D) 500B + 300M ≤ 18000
E) 300B + 500M ≤ 18000
73) The __________ property of linear programming models indicates that the decision variables cannot be restricted to integer values and can take on any fractional value.
A) linearity
C) divisibility
D) certainty
E) proportionality
74) The __________ property of linear programming models indicates that the rate of change or slope of the objective function or a constraint is constant.
B) divisibility
C) certainty
D) proportionality
E) feasibility
75) The __________ property of linear programming models indicates that the values of all the model parameters are known and are assumed to be constant.
B) divisibility
C) certainty
D) proportionality
76) The region which satisfies all of the constraints in a graphical linear programming problem is called the
A) region of optimality
B) feasible solution space
C) region of non-negativity
D) optimal solution space
77) Which of the following statements is not true?
A) An infeasible solution violates all constraints.
B) A feasible solution point does not have to lie on the boundary of the feasible solution.
C) A feasible solution satisfies all constraints.
D) An optimal solution satisfies all constraints.
78) Except satisfying the non-negativity constraint, a solution that satisfies all the other constraints of a linear programming problem is called
A) feasible
B) infeasible
C) semi-feasible
D) optimal
79) The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are \$3.00 per case and profits for diet soft drink are \$2.00 per case. Which of the following is not a feasible production combination?
A) 90R and 75D
B) 135R and 0D
C) 0R and 120D
D) 75R and 90D
E) 40R and 100D
80) The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are \$3.00 per case and profits for diet soft drink are \$2.00 per case. What are the optimal daily production quantities of each product and the optimal daily profit?
A) R = 75, D = 90, Z = \$405
B) R = 135, D = 0, Z = \$405
C) R = 0, D= 120, Z = \$360
D) R = 90, D = 75, Z = \$420
E) R = 40, D= 100, Z = \$320
81) __________ is used to analyze changes in model parameters.
A) Optimal solution
B) Feasible solution
C) Sensitivity analysis
D) none of the above
82) Cully furniture buys 2 products for resale: big shelves (B)and medium shelves (M).Each big shelf costs \$500 and requires 100 cubic feet of storage space, and each medium shelf costs \$300 and requires 90 cubic feet of storage space. The company has \$75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is \$300 and for each medium shelf is \$150. Which of the following is not a feasible purchase combination?
A) 0 big shelves and 200 medium shelves
B) 100 big shelves and 82 medium shelves
C) 150 big shelves and 0 medium shelves
D) 100 big shelves and 100 medium shelves
E) 100 big shelves and 0 medium shelves
83) Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs \$500 and requires 100 cubic feet of storage space, and each medium shelf costs \$300 and requires 90 cubic feet of storage space. The company has \$75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is \$300 and for each medium shelf is \$150. What is the maximum profit?
A) \$25000
B) \$35000
C) \$45000
D) \$55000
E) \$65000
84) Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs \$500 and requires 100 cubic feet of storage space, and each medium shelf costs \$300 and requires 90 cubic feet of storage space. The company has \$75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is \$300 and for each medium shelf is \$150. In order to maximize profit, how many big shelves (B) and how many medium shelves (M) should be purchased?
A) B = 90, M = 75
B) B = 135, M = 15
C) B = 150, M = 0
D) B = 0, M = 200
E) B = 100, M = 100
85) The theoretical limit on the number of constraints that can be handled by a linear programming problem is
A) 2
B) 3
C) 4
D) unlimited
86) Consider the following maximization problem.
MAX z = x + 2y
s.t. 2x + 3y ≤ 6
5x + 6y ≤ 30
y ≥ 1
The optimal solution
A) cannot be determined
B) occurs where x = 4.67 and y = 1.11
C) occurs where x = 0 and y = 5
D) occurs where x = 6 and y = 0
E) results in an objective function value of 12
The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*.

87) This linear programming problem is a:
A) maximization problem
B) minimization problem
C) irregular problem
D) cannot tell from the information given
88) The equation for constraint DH is:
A) 4X + 8Y ≥ 32
B) 8X + 4Y ≥ 32
C) X + 2Y ≥ 8
D) 2X + Y ≥ 8
E) None of the above
89) Which of the following points are not feasible?
A) A
B) J
C) H
D) G
E) B
Diff: 1 Page Ref: 54
Main Heading: Graphical Solutions of Linear Programming Models
Key words: graphical solution, feasible point
90) Which line is represented by the equation 2X + Y ≥ 8?
A) BF
B) CG
C) DH
D) AJ
91) Which of the following constraints has a surplus greater than 0?
A) BF
B) CG
C) DH
D) AJ
92) The constraint AJ
A) Is not a binding constraint.
B) Has no surplus
C) Does not contain feasible points
D) A and B
E) B and C
93) Multiple optimal solutions can occur when the objective function is __________ a constraint line.
A) unequal to
B) equal to
C) perpendicular to
D) parallel to
94) A slack variable
A) is the amount by which the left side of a ≥ constraint is larger than the right side
B) is the amount by which the left side of a ≤ constraint is smaller than the right side
C) is the difference between the left and right side of a constraint
D) exists for each variable in a linear programming problem
95) The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are \$3.00 per case and profits for diet soft drink are \$2.00 per case. For the production combination of 135 cases of regular and 0 cases of diet soft drink, which resources will not be completely used?
A) only time
B) only syrup
C) time and syrup
D) neither time nor syrup
96) Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs \$500 and requires 100 cubic feet of storage space, and each medium shelf costs \$300 and requires 90 cubic feet of storage space. The company has \$75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is \$300 and for each medium shelf is \$150. If the furniture company purchases no big shelves and 200 medium shelves, which of the two resources will be completely used (at capacity)?
A) investment money only
B) storage space only
C) investment money and storage space
D) neither investment money nor storage space
97) Consider the following linear program:
MAX z = 5x + 3y
s.t. x – y ≤ -1
x ≤ 1
The optimal solution
A) is infeasible
B) occurs where x = 1 and y = 0
C) occurs where x = 0 and y = 1
D) results in an objective function value of 11
98) The first step in solving a graphical linear programming model is
A) plot the model constraints as equations on the graph and indicate the feasible solution area
B) plot the objective function and move this line out from the origin to locate the optimal solution point
C) solve simultaneous equations at each corner point to find the solution values at each point
D) determine which constraints are binding
99) The optimal solution of a minimization problem is at the extreme point __________ the origin.
A) farthest from
B) closest to
C) exactly at
D) parallel to
100) Multiple optimal solutions provide __________ flexibility to the decision maker.
A) greater
B) less
C) greater or equal
D) less or equal
101) Which of the following special cases does not require reformulation of the problem in order to obtain a solution?
A) unboundedness
B) infeasibility
C) alternate optimality
D) each one of these cases requires reformulation
102) If the feasible region for a linear programming problem is unbounded, then the solution to the corresponding linear programming problem is __________ unbounded.
A) always
B) sometimes
C) never
D) there is not enough information to complete this statement
Introduction to Management Science, 10e (Taylor)
Chapter 3 Linear Programming: Computer Solution and Sensitivity Analysis

1) The reduced cost (shadow price) for a positive decision variable is 0.
2) When the right-hand sides of 2 constraints are both increased by 1 unit, the value of the objective function will be adjusted by the sum of the constraints’ prices.
3) When a linear programming problem is solved using a computer package decision variables will always be integer and therefore decision variable values never need to be rounded.
4) Sensitivity ranges can be computed only for the right hand sides of constraints.
5) Sensitivity analysis determines how a change in a parameter affects the optimal solution.
6) The sensitivity range for an objective function coefficient is the range of values over which the current optimal solution point (product mix) will remain optimal.
7) The sensitivity range for an objective function coefficient is the range of values over which the profit does not change.
8) The sensitivity range for a constraint quantity value is the range over which the shadow price is valid.
9) If we change the constraint quantity to a value outside the sensitivity range for that constraint quantity, the shadow price will change.
10) The sensitivity range for a constraint quantity value is the range over which the optimal values of the decision variables do not change.
11) Linear programming problems are restricted to decisions in a single time period.
12) A maximization problem may be characterized by all greater than or equal to constraints.
13) A change in the value of an objective function coefficient will always change the value of the optimal solution.
14) The terms reduced cost, shadow price, and dual price all mean the same thing.
15) Sensitivity analysis can be used to determine the effect on the solution for changing several parameters at once.
16) For a profit maximization problem, if the allowable increase for a coefficient in the objective function is infinite, then profits are unbounded.
17) The reduced cost (shadow price) for a positive decision variable is __________.
18) The sensitivity range for a __________ is the range of values over which the quantity values can change without changing the shadow price
19) __________ is the analysis of the effect of parameter changes on the optimal solution.
20) The sensitivity range for a constraint quantity value is also the range over which the __________ is valid.
21) The sensitivity range for an __________ coefficient is the range of values over which the current optimal solution point (product mix) will remain optimal.
Consider the following linear program, which maximizes profit for two products, regular (R), and super (S):
MAX 50R + 75S
s.t.
1.2R + 1.6 S ≤ 600 assembly (hours)
0.8R + 0.5 S ≤ 300 paint (hours)
.16R + 0.4 S ≤ 100 inspection (hours)
22) The optimal number of regular products to produce is __________, and the optimal number of super products to produce is __________, for total profits of __________.
23) If the company wanted to increase the available hours for one of their constraints (assembly, painting, or inspection ) by 2 hours, they should increase __________.
24) The profit on the super product could increase by __________ without affecting the product mix.
25) If downtime reduced the available capacity for painting by 40 hours (from 300 to 260 hours), profits would be reduced by __________.
26) A change in the market has increased the profit on the super product by \$5. Total profit will increase by __________.
Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of \$30 on each tractor and \$30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table.

27) How many tractors and saws should be produced to maximize profit, and how much profit will they make?
28) Determine the sensitivity range for the profit for tractors.
29) What is the shadow price for assembly?
30) What is the shadow price for fabrication?
31) What is the maximum amount a manager would be willing to pay for one additional hour of machining time?
32) A breakdown in fabrication causes the available hours to drop from 120 to 90 hours. How will this impact the optimal number of tractors and mowers produced?
33) What is the range for the shadow price for assembly?
The production manager for the Whoppy soft drink company is considering the production of 2 kinds of soft drinks: regular (R) and diet (D). The company operates one “8 hour” shift per day. Therefore, the production time is 480 minutes per day. During the production process, one of the main ingredients, syrup is limited to maximum production capacity of 675 gallons per day. Production of a regular case requires 2 minutes and 5 gallons of syrup, while production of a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are \$3.00 per case and profits for diet soft drink are \$2.00 per case.
34) What is the optimal daily profit?
35) How many cases of regular and how many cases of diet soft drink should Whoppy produce to maximize daily profit?
36) What is the sensitivity range for the per case profit of a diet soft drink?
37) What is the sensitivity range of the production time?
38) if the company decides to increase the amount of syrup it uses during production of these soft drinks to 990 lbs. will the current product mix change? If show what is the impact on profit?
39) What is the optimal product mix and maximum profit?
40) Determine the sensitivity range for the profit on the big shelf.
41) If the Mallory Furniture is able to increase the profit per medium shelf to \$200, would the company purchase medium shelves. If so, what would be the new product mix and the total profit?
The linear programming problem whose output follows is used to determine how many bottles of fire red nail polish (x1), bright red nail polish (x2), basil green nail polish(x3), and basic pink nail polish(x4) a beauty salon should stock. The objective function measures profit; it is assumed that every piece stocked will be sold. Constraint 1 measures display space in units, constraint 2 measures time to set up the display in minutes. Note that green nail polish does not require any time to prepare its display. Constraints 3 and 4 are marketing restrictions. Constraint 3 indicates that the maximum demand for fire red and green polish is 25 bottles, while constraint 4 specifies that the minimum demand for bright red, green and pink nail polish bottles combined is at least 50 bottles.
42) How much space will be left unused? How many minutes of idle time remaining for setting up the display?
43) a) To what value can the per bottle profit on fire red nail polish drop before the solution (product mix) would change?
b) By how much can the per bottle profit on green basil nail polish increase before the solution (product mix) would change?
44) a) By how much can the amount of space decrease before there is a change in the profit?
b) By how much can the amount of space decrease before there is a change in the product mix?
c) By how much can the amount of time available to setup the display can increase before the solution (product mix) would change?
d) What is the lowest value for the amount of time available to setup the display before the solution (product mix) would change?
45) You are offered the chance to obtain more space. The offer is for 15 units and the total price is \$1500. What should you do? Why?
46) Max Z = 5×1 + 3×2
Subject to: 6×1 + 2×2 ≤ 18
15×1 + 20×2 ≤ 60
x1 + x2 ≥ 0
Determine the sensitivity range for each constraint.
47) Max Z = 5×1 + 3×2
Subject to: 6×1 + 2×2 ≤ 18
15×1 + 20×2 ≤ 60
x1 + x2 ≥ 0
Determine the sensitivity range for each objective function coefficient.
48) Max Z = 3×1 + 3×2
Subject to: 10×1 + 4×2 ≤ 60
25×1 + 50×2 ≤ 200
x1 , x2 ≥ 0
Determine the sensitivity range for each objective function coefficient.
49) For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs., and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the:
A) same product mix, different total profit
B) different product mix, same total profit as before
C) same product mix, same total profit
D) different product mix, different total profit
50) A plant manager is attempting to determine the production schedule of various products to maximize profit. Assume that a machine hour constraint is binding. If the original amount of machine hours available is 200 minutes., and the range of feasibility is from 130 minutes to 340 minutes, providing two additional machine hours will result in:
A) the same product mix, different total profit
B) a different product mix, same total profit as before
C) the same product mix, same total profit
D) a different product mix, different total profit
The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are \$2 per bottle, and profits for dark beer are \$1 per bottle.
51) If the production manager decides to produce of 0 bottles of light beer and 400 bottles of dark beer, it will result in slack of
A) malt only
B) wheat only
C) both malt and wheat
D) neither malt nor wheat
52) Which of the following is not a feasible solution?
A) 0 L and 0 D
B) 0 L and 400 D
C) 200 L and 300 D
D) 400 L and 400 D
53) What is the optimal weekly profit?
A) \$1000
B) \$900
C) \$800
D) \$700
E) \$600
Mallory Furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs \$500 and requires 100 cubic feet of storage space, and each medium shelf costs \$300 and requires 90 cubic feet of storage space. The company has \$75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is \$300 and for each medium shelf is \$150.
54) Which of the following is not a feasible purchase combination?
A) 0 big shelves and 200 medium shelves
B) 0 big shelves and 0 medium shelves
C) 150 big shelves and 0 medium shelves
D) 100 big shelves and 100 medium shelves
55) If the Mallory Furniture company decides to purchase 150 big shelves and no medium shelves, which of the two resources will be left over?
A) investment money only
B) storage space only
C) investment money and storage space
D) neither investment money nor storage space
The production manager for the Whoppy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. The company operates one “8 hour” shift per day. Therefore, the production time is 480 minutes per day. During the production process, one of the main ingredients, syrup is limited to maximum production capacity of 675 gallons per day. Production of a regular case requires 2 minutes and 5 gallons of syrup, while production of a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are \$3.00 per case and profits for diet soft drink are \$2.00 per case.
56) Which of the following is not a feasible production combination?
A) 90 R and 75 D
B) 135 R and 0 D
C) 0 R and 120 D
D) 75 R and 90 D
E) 50 R and 50 D
57) For the production combination of 135 regular cases and 0 diet cases, which resource is completely used up (at capacity)?
A) only time
B) only syrup
C) time and syrup
D) neither time nor syrup
58) The sensitivity range for the profit on a regular case of soda is
A) \$2 to \$3
B) \$2 to \$4
C) \$1 to \$3
D) \$1 to \$3.33
59) Which of the following could not be a linear programming problem constraint?
A) A + B ≤ -3
B) A – B ≤ -3
C) A – B ≤ 3
D) A + B ≥ -3
E) -A + B ≤ -3
60) Use the constraints given below and determine which of the following points is feasible.
(1) 14x + 6y ≤ 42
(2) x – y ≤ 3
A) x = 1; y = 5
B) x = 2; y = 2
C) x = 2; y = 8
D) x = 2; y = 4
E) x = 3; y = 0.5
61) For the constraints given below, which point is in the feasible region of this minimization problem?
(1) 14x + 6y ≤ 42
(2) x + 3y ≥ 6
A) x = 0; y = 4
B) x = 2; y = 5
C) x = 1; y = 2
D) x = 2; y = 1
E) x = 2; y = 3
62) What combination of x and y is a feasible solution that minimizes the value of the objective function ?
Min Z = 3x + 15y
(1) 2x + 4y ≥ 12
(2) 5x + 2y ≥10
A) x = 0; y = 3
B) x = 0; y = 5
C) x = 5; y = 0
D) x = 6; y = 0
E) x = 4; y = 1
63) A shadow price reflects which of the following in a maximization problem?
A) the marginal gain in the objective that would be realized by adding 1 unit of a resource
B) the marginal gain in the objective that would be realized by subtracting 1 unit of a resource
D) the marginal gain of selling one more unit
64) Given the following linear programming problem:
Max Z = 15x + 20 y
s.t.
8x + 5y ≤ 40
4x + y ≥ 4
What would be the values of x and y that will maximize revenue?
A) x = 5; y = 0
B) x = 0; y = 8
C) x = 0; y = 1
D) x = 1; y = 0
E) x = 3; y = 4
65) Given the following linear program that maximizes revenue:
Max Z = 15x + 20 y
s.t.
8x + 5y ≤ 40
4x + y ≥ 4
What is the maximum revenue at the optimal solution?
A) \$120
B) \$160
C) \$185
D) \$200
Given the following linear programming problem that minimizes cost.
Min Z = 2x + 8y
Subject to (1) 8x + 4y ≥ 64
(2) 2x + 4y ≥ 32
(3) y ≥ 2

66) Determine the optimum values for x and y.
A) x = 2; y = 6
B) x = 6; y = 2
C) x = 12; y = 2
D) x = 2; y = 2
E) x = 6; y = 5
67) At the optimal solution the minimum cost is:
A) \$30
B) \$40
C) \$50
D) \$52
E) \$53.33
68) What is the sensitivity range for the cost of x?
A) 0 to 2
B) 4 to 6
C) 2 to 4
D) 0 to 4
Diff: 2 Page Ref: 81
Main Heading: Sensitivity Analysis and Computer Solution
Key words: sensitivity analysis/range for objective function coefficients
69) What is the sensitivity range for the third constraint, y ≥ 2?
A) 0 to 4
B) 2 to 5.33
C) 0 to 5.33
D) 4 to 6.33
70) For a maximization problem, the shadow price measures the __________ in the value of the optimal solution, per unit increase for a given __________.
A) decrease, resource
B) increase, parameter
C) improvement, resource
D) change, objective function coefficient
E) decrease, parameter
71) Sensitivity analysis is the analysis of the effect of __________ changes on the __________.
A) price, company
B) cost, production
C) parameter, optimal solution
D) none of the above
72) For a linear programming problem, assume that a given resource has not been fully used. We can conclude that the shadow price associated with that constraint:
A) will have a positive value
B) will have a negative value
C) will have a value of zero
D) could have a positive, negative or a value of zero. (no sign restrictions)
Diff: 3 Page Ref: 90
Key words: sensitivity analysis, shadow price
73) For a resource constraint, either its slack value must be __________ or its shadow price must be __________.
A) negative, negative
B) negative, zero
C) zero, zero
D) zero, negative
Aunt Anastasia operates a small business: she produces seasonal ceramic objects to sell to tourists. For the spring, she is planning to make baskets, eggs, and rabbits. Based on your discussion with your aunt you construct the following table.
Your aunt also has committed to make 25 rabbits for a charitable organization. Based on the information in the table, you formulate the problem as a linear program.
74) Which additional resources would you recommend that Aunt Anastasia try to obtain?
A) mix/mold
B) kiln
C) paint and seal
D) demand
E) Cannot tell from the information provided
75) Suppose the charitable organization contacted Aunt Anastasia and told her that they had overestimated the amount of rabbits they needed. Instead of 25 rabbits, they need 35. How would this affect Aunt Anastasia’s profits?
A) Profits would increase by \$5.
B) Profits would decrease by \$5
C) Profits would increase by \$2.50
D) Profits would decrease by \$2.50
E) Cannot tell from the information provided.
76) Aunt Anastasia feels that her prices are too low, particularly for her eggs. How much would her profit have to increase on the eggs before it is profitable for her to make and sell eggs?
A) \$0.50
B) \$1.00
C) \$1.50
D) \$2.50
E) None of the above
77) Aunt Anastasia’s available hours for paint and seal have fallen from 80 hours to 60 hours because of other commitments. How will this affect her profits?
A) Profits will decrease by \$30.
B) Profits will increase by \$30.
C) Profits will decrease by \$20.
D) Profits will increase by \$20.
E) Profits will not change.
78) Aunt Anastasia can obtain an additional 10 hours of kiln capacity free of charge from a friend. If she did this, how would her profits be affected?
A) Profit would increase by \$25.
B) Profits would decrease by \$25.
C) Profits would increase by \$6.25.
D) Profits would decrease by \$6.25
E) Cannot tell from the information provided.
79) Aunt Anastasia is planning for next spring, and she is considering making only 2 products. Based on the results from the linear program, which two products would you recommend that she make?
C) eggs and rabbits
D) She should continue to make all 3.
E) Cannot tell from the information provided.
Billy’s Blues sells 3 types of T-shirts: Astro, Bling, and Curious. Manufacturing Astros requires 2 minutes of machine time, 20 minutes of labor, and costs \$10. Brand Bling requires 2..5 minutes of machine time, 30 minutes of labor, and costs \$14 to produce. Brand Curious requires 3 minutes of machine time, 45 minutes of labor, and costs \$18 to produce. There are 300 machining hours available per week, 3,750 labor hours, and he has a budget of \$3,000. Brand Astro sells for \$15, Brand Bling for \$18, and Brand Curious for \$25.
80) If Billy could acquire more of any resource, which would it be?
A) machining time
B) labor time
C) money
81) If one of Billy’s machines breaks down, it usually results in about 6 hours of downtime. When this happens, Billy’s profits are reduced by
A) \$15
B) 18
C) \$25
D) \$35
82) Billy’s accountant made an error, and the budget has been reduced from \$3000 to \$2500. Billy’s profit will go down by
A) \$0
B) \$625
C) \$1350
D) \$1650
83) Billy has decided that he can raise the price on the Curious t-shirt by 10% without losing sales. If he raises the price, his profits will
A) increase by 10%
B) decrease by 10%
C) increase by \$2.50
D) increase by \$125
Introduction to Management Science, 10e (Taylor)
Chapter 4 Linear Programming: Modeling Examples

1) When formulating a linear programming problem constraint, strict inequality signs (i.e., less than < or, greater than >) are not allowed.
2) When formulating a linear programming model on a spreadsheet, the measure of performance is located in the target cell.
3) The standard form for the computer solution of a linear programming problem requires all variables to be to the right and all numerical values to be to the left of the inequality or equality sign
4) The standard form for the computer solution of a linear programming problem requires all variables to be on the left side, and all numerical values to be on the right side of the inequality or equality sign.
5) Fractional relationships between variables are not permitted in the standard form of a linear program.
6) A constraint for a linear programming problem can never have a zero as its right-hand-side value.
7) The right hand side of constraints cannot be negative.
8) A systematic approach to model formulation is to first define decision variables.
9) A systematic approach to model formulation is to first construct the objective function before determining the decision variables.
10) In a linear programming model, a resource constraint is a problem constraint with a greater-than-or-equal-to (≥) sign.
11) Determining the production quantities of different products manufactured by a company based on resource constraints is a product mix linear programming problem.
12) Product mix problems cannot have “greater than or equal to” (≥) constraints.
13) When using a linear programming model to solve the “diet” problem, the objective is generally to maximize profit.
14) When using a linear programming model to solve the “diet” problem, the objective is generally to maximize nutritional content.
15) In formulating a typical diet problem using a linear programming model, we would expect most of the constraints to be related to calories.
16) Solutions to diet problems in linear programming are always realistic.
17) Diet problems usually maximize nutritional value.
18) In most media selection decisions, the objective of the decision maker is to minimize cost.
19) In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the audience exposure.
20) Linear programming model of a media selection problem is used to determine the relative value of each advertising media.
21) In a media selection problem, maximization of audience exposure may not result in maximization of total profit.
22) In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities.
23) In an unbalanced transportation model, supply does not equal demand and supply constraints have ≤ signs.
24) Transportation problems can have solution values that are non-integer and must be rounded.
25) In a transportation problem, the supply constraint represents the maximum amount of product available for shipment or distribution at a given source (plant, warehouse, mill).
26) In a transportation problem, a supply constraint (the maximum amount of product available for shipment or distribution at a given source) is a greater-than-or equal-to constraint (≥).
27) In a transportation problem, a demand constraint for a specific destination represents the amount of product demanded by a given destination (customer, retail outlet, store).
28) In a transportation problem, a demand constraint (the amount of product demanded at a given destination) is a less-than-or equal-to constraint (≤).
29) Blending problems usually require algebraic manipulation in order to write the LP in “standard form.”
30) Data Envelopment Analysis indicates which type of service unit makes the highest profit.
31) Data Envelopment Analysis indicates the the relative _________ of a service unit compared with others.
32) __________ types of linear programming problems often result in fractional relations between variables which must be eliminated.
33) When formulating a linear programming model on a spreadsheet, the measure of performance is located in the __________ cell.
34) When the __________ command is used in an Excel spreadsheet, all the values in a column (or row) are multiplied by the values in another column (or row) and then summed.
35) For product mix problems, the constraints are usually associated with __________.
36) The __________ for the computer solution of a linear programming problem requires all variables on the left side, and all numerical values on the right side of the inequality or equality sign.
37) The objective function of a diet problem is usually to __________ subject to nutritional requirements.
38) Investment problems maximize __________.
39) In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the __________.
40) In __________ problem, maximization of audience exposure may not result in maximization of total profit.
41) In a balanced transportation model, supply equals __________ .
42) In a __________ transportation problem, supply exceeds demand.
The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar (V). He has a limited amount of the 3 ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of Lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of Vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of Lime chips are \$0.40, and for a bag of Vinegar chips \$0.50.
43) What is the formulation for this problem?
44) For the production combination of 800 bags of Lime and 600 bags of Vinegar, which resource is not completely used up and how much is remaining?
45) For the production combination of 800 bags of Lime and 600 bags of Vinegar, which resource is not completely used up and how much is remaining?
A croissant shop produces 2 products: bear claws (B) and almond filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS (tablespoons) of almond paste. An almond- filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today’s production run. The shop must produce at least 400 almond filled croissants due to customer demand. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each.
46) This represents what type of linear programming application?
47) What is the formulation for this problem?
48) For the production combination of 600 bear claws and 800 almond filled croissants, how much flour and almond paste is remaining?
49) If Xij = the production of product i in period j, write an expression to indicate that the limit on production of the company’s 3 products in period 2 is equal to 400.
50) Small motors for garden equipment is produced at 4 manufacturing facilities and needs to be shipped to 3 plants that produce different garden items (lawn mowers, rototillers, leaf blowers). The company wants to minimize the cost of transporting items between the facilities, taking into account the demand at the 3 different plants, and the supply at each manufacturing site. The table below shows the cost to ship one unit between each manufacturing facility and each plant, as well as the demand at each plant and the supply at each manufacturing facility.
Write the formulation for this problem.
51) Quickbrush Paint Company makes a profit of \$2 per gallon on its oil-base paint and \$3 per gallon on its water-base paint. Both paints contain two ingredients, A and B. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. The company wishes to use linear programming to determine the appropriate mix of oil-base and water-base paint to produce to maximize its total profit. How much oil based and water based paint should the Quickbrush make?
Andy Tyre manages Tyre’s Wheels, Inc. Andy has received an order for 1000 standard wheels and 1200 deluxe wheels next month, and for 750 standard wheels and 1000 deluxe wheels the following months. He must fill all the orders. The cost of regular time production for standard wheels is \$25 and for deluxe wheels, \$40. Overtime production costs 50% more. For each of the next two months there are 1000 hours of regular time production and 500 hours of overtime production available. A standard wheel requires .5 hours of production time and a deluxe wheel, .6 hours. The cost of carrying a wheel from one month to the next is \$2.
52) Define the decision variables and objective function for this problem.
53) Write the constraints for this problem.
Bullseye Shirt Company makes three types of shirts: Athletic, Varsity, and Surfer. The shirts are made from different combinations of cotton and rayon. The cost per yard of cotton is \$5 and the cost for rayon is \$7. Bullseye can receive up to 4,000 yards of cotton and 3,000 yards of rayon per week.
The table below shows relevant manufacturing information:
Shirt Total Yards of fabric per shirt Fabric requirement Minimum weekly contracts Maximum Demand Selling Price
Athletic 1.00 at least 60% cotton 500 600 \$30
Varsity 1.20 no more than 30% rayon 650 850 \$40
Surfer 0.90 As much as 80% cotton 300 700 \$36
54) Assume that the decision variables are defined as follows:
A = total number of athletic shirts produced
V = total number of varsity shirts produced
S = total number of surfer shirts produced
C = yards of cotton purchased
R = yards of rayon purchased
Xij = yards of fabric i (C or R) blended into shirt J (A, V or S)
Write the objective function.
55) Write the constraints for the fabric requirements.
56) Write the constraints for the total number of shirts of each style produced.
57) Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel’s cat food is made by mixing two types of cat food to obtain the “nutritionally balanced cat diet.” The data for the two cat foods are as follows:
58) A credit union wants to make investments in the following:
The firm will have \$2,500,000 available for investment during the coming year. The following restrictions apply:
∙ Risk free securities may not exceed 30% of the total funds, but must comprise at least 5% of the total.
∙ Signature loans may not exceed 12% of the funds invested in all loans (vehicle, consumer, other secured loans, and signature loans)
∙ Consumer loans plus other secured loans may not exceed the vehicle loans
∙ Other secured loans plus signature loans may not exceed the funds invested in risk free securities. How should the \$2,500,000 be allocated to each alternative to maximize annual return? What is the annual return?
59) When systematically formulating a linear program, the first step is
A) Construct the objective function
B) Formulate the constraints
C) Identify the decision variables
D) Identify the parameter values
E) Identify a feasible solution
60) The following types of constraints are ones that might be found in linear programming formulations:
1. ≤
2. =
3. >
A) 1 and 2
B) 2 and 3
C) 1 and 3
D) all of the above
61) Assume that x2, x7 and x8 are the dollars invested in three different common stocks from New York stock exchange. In order to diversify the investments, the investing company requires that no more than 60% of the dollars invested can be in “stock two”. The constraint for this requirement can be written as:
A) x2 ≥ .60
B) x2 ≥ .60 (x2 + x7 + x8)
C) .4×2 – .6×7 – .6×8 ≤ 0
D) .4×2 – .6×7 – .6×8 ≥ 0
E) -.4×2 + .6×7 + .6×8 ≤ 0
62) The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient.
Ingredient Percent per pound in Feed A Percent per pound in Feed B Minimum daily requirement (pounds)
1 20 24 30
2 30 10 50
3 0 30 20
4 24 15 60
5 10 20 40
The constraint for ingredient 3 is:
A) .5A + .75B = 20
B) .3B = 20
C) .3 B≤ 20
D) .3B ≥ 20
E) A + B = .3(20)
The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar (V). He has a limited amount of the 3 ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of Lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of Vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of Lime chips are \$0.40, and for a bag of Vinegar chips \$0.50.
63) For the production combination of 800 bags of Lime and 600 bags of Vinegar, which of the three resources is (are) not completely used?
A) flour only
B) salt only
C) herbs only
D) salt and flour
E) salt and herbs
64) What is the constraint for salt?
A) 6L + 8V ≤ 4800
B) 1L + 2V ≤ 4800
C) 3L + 2V ≤ 4800
D) 2L + 3V ≤ 4800
E) 2L + 1V ≤ 4800
Diff: 2 Page Ref: 111-116
Key words: formulation, constraint
65) Which of the following is not a feasible production combination?
A) 0L and 0V
B) 0L and 1000V
C) 1000L and 0V
D) 0L and 1200V
66) If Xab = the production of product a in period b, then to indicate that the limit on production of the company’s “3” products in period 2 is 400,
A) X32 ≤ 400
B) X21 + X22 + X23 ≤ 400
C) X12 + X22 + X32 ≤ 400
D) X12 + X22 + X32 ≥ 400
E) X23 ≤ 400
67) Balanced transportation problems have the following type of constraints:
A) ≥
B) ≤
C) =
E) none of the above
68) The majority of the goal constraints are equalities that include __________ variables.
A) only deviational
B) deviational and decision
C) only decision
D) neither deviational nor decision variables
E) undeviational
69) A __________ deviational variable is the amount by which a goal level is underachieved.
A) negative
B) positive
C) positive or negative
D) positive and negative
70) The objective function in a goal programming model seeks to __________ the deviation from goals in the order of the goal priorities.
A) free
B) even out
C) maximize
D) minimize
71) Goal constraints can include __________ deviational variables.
A) no
B) some
C) all
D) multiple
72) Deviational variables in a goal programming model constraint represent the
A) underachievement or overachievement of a goal level
B) resource constraint as defined by the linear model
C) probability of an optimal solution
D) probabilistic variables in the objective constraints
73) Two or more goals at the same priority level can be assigned weights to indicate their relative
A) meaning
B) slack
C) difference
D) importance
74) A company has 3 goals, listed in order of importance.
1. Achieve a total profit of at least \$240 million.
2. Maintain the current employment level of 3,000 employees
3. Invest no more than \$70 million in capital.
What is the objective function for a goal program for this situation?
A) P1d1- , P2d2- , P3d3+
B) P1d1- , P2d2+ , P2d2- , P3d3-
C) P1d1- , P2d2- , P2d2- , P3d3+
D) P1d1+ , P2d2- , P2d2- , P3d3+
E) None of the above
75) If the constraint 3×1 + 4×2 + (d1-) – (d1+) = 250 measures hours, then
A) 3×1 + 4×2 is equal to the actual time spent
B) if d1- is equal to 25, then 3×1 + 4×2 must equal 225.
C) overtime could be represented by d1+
D) all of the above are true.
76) A company has a goal to maintain the currently employment level, but places more importance on laying employees off than on hiring new employees. In other words, the company would rather hire than lay off employees. If the company assigns a “penalty weight” of 4 for the amount under the employment goal (goal 2) , and a weight of 2 for the amount over the employment goal, how would this be expressed in the objective function?
A) Min 4P2d2- + 2P2d2+
B) Min 2P2d2- + 4P2d2+
C) Max 4P2d2- + 2P2d2+
D) Min 4P2d2+ + 2P2d2-
E) None of the above
77) A company has a goal of calling on at least 400 customers a month (goal 1), but no fewer than 260 customers a month (goal 2). If X represents the number of customers contacted, which pair of constraints listed below is the appropriate representation in a goal programming problem?
A) X + d1- – d1+ = 400, X + d2- – d2+ = 260
B) X – d1- + d1+ = 400, X – d2- – d2+ = 260
C) X – d1- + d1+ = 400, X + d2- – d2+ = 260
D) X + d1- – d1+ = 400, X – d2- + d2+ = 260
78) Consider the following constraint: 2×1 + 3×2 =60. Assume that we convert this constraint into a goal constraint and the value of x1 = 15 and the value of x2 = 15, then the values of d1+ and d1- are __________ and __________ respectively.
A) 0, 15
B) 15, 0
C) 20, 0
D) 0, 20
E) 15, 15
79) One goal __________ achieved at the expense of another higher-priority goal.
A) is never
B) can sometimes be
C) is always
D) is under certain circumstances
80) The objective function in all goal programming models is to __________ from the goal constraint levels.
A) maximize alternatives
B) minimize alternatives
C) minimize deviation
D) maximize deviation
81) Goal programming solutions __________ achieve all goals.
A) always
B) don’t always
C) sometimes
D) never
Riverside Industries makes two products and each product is processed in three departments. The time requirements for each product in each department are given below. The profit for each product is also provided as well as the available hours in each department.
Product Department A Department B Department C Profit
1 3 4 2 1
2 2 1 2 2
Available Hours 600 400 400
Management wants to achieve 3 goals. The first two goals are equal in priority.
Priority 1: Produce at least 125 units of product 1.
Priority 1: Produce at least 80 units of product 2.
Priority 2: Achieve a profit of at least 300.
82) The goal programming model for this problem has how many constraints?
A) 3
B) 4
C) 6
D) 7
83) The goal programming constraint for the first goal is:
A) 3×1 + d1- – d1+ = 125
B) 3×1 – d1- + d1+ = 125
C) 1×1 + d1- – d1+ = 125
D) 1×1 – d1- + d1+ = 125
84) The objective function for this goal program is:
A) Min P1d1- + P1d2-, P2d3-
B) Min P1d1+ + P1d2-, P2d3-
C) Min P1d1- + P1d2+, P2d3-
D) Min P1d1- + P1d2-, P2d3+
85) If the second goal was to produce no more than 80 units of product two, the objective function would be:
A) Min P1d1- + P1d2-, P2d3-
B) Min P1d1+ + P1d2-, P2d3-
C) Min P1d1- + P1d2+, P2d3-
D) Min P1d1- + P1d2-, P2d3+
86) Goal programming solutions achieve the __________ satisfactory solution possible.
A) best or most
B) worst or least
C) only
D) somewhat
87) If choice A is strongly preferred to choice B and choice B is moderately preferred to choice C, and the decision maker says choice C is equally preferred to choice A, what conclusion can be drawn?
A) The decision maker is consistent.
B) The decision maker is inconsistent.
C) The pairwise comparison matrix is symmetric.
D) The decision maker has already synthesized.
88) In a pairwise comparison, __________ alternatives are compared according to a criterion and one is preferred.
A) 6
B) 4
C) 8
D) 2
89) In synthesization, decision alternatives are prioritized __________ criteria/ion.
A) within some
B) among some
C) among all
D) within each
90) Pairwise comparisons are made among
A) all alternatives for a particular criterion
B) all alternatives for all criteria
C) some alternatives for a particular criterion
D) some alternatives for all criteria
91) In a pairwise comparison matrix the diagonal values will __________ equal __________.
A) sometimes, 1
B) always, 0
C) sometimes, 0
D) always, 1
E) none of the above
92) The analytic hierarchy process
A) optimizes procedures with a single goal
B) requires no pairwise comparison
C) uses both qualitative and subjective assessment
D) does not require the input of a decision maker
93) In determining the pair wise comparison matrix, if the decision maker rates the option A compared to option B as “4”, then option B compared to option A __________.
A) would have to be also Answered by the decision maker
B) is also 4
C) 1/4
D) 2
E) would have to be computed by making various calculations based on other values in the pairwise comparison matrix
94) The analytical hierarchy process is a method for __________ decision alternatives.
A) creating
B) ranking
C) changing
D) deleting
95) Values with an acceptable consistency ratio are values
A) less than or equal to 0.1
B) greater than 0.5 but less than 0.6
C) less than 1 but greater than 0.5
D) greater than 0.2 but less than 0.5
96) Assume that a decision maker has to make a choice between three types of cars. Chevy, Honda, and Ford. Based on three criteria: comfort, MPG and style.
The row averages for criteria is summarized in the following column vector:
The preference matrix for the three types of cars is given as follows:
The first row of the following matrix represents Chevy, the second row represents Honda, and the third row represents Ford.
Compute the overall score for each decision alternative (car). Which choice does the decision maker prefer?
A) Chevy
B) Honda
C) Ford
D) Honda and Chevy are equally preferred
E) Ford and Chevy are equally preferred
97) Assume that a plant manager has to decide where to locate its warehouse The decision has been narrowed down to choices among the following three cities: Detroit, Michigan, Cleveland, Ohio and St. Louis Missouri. The following pairwise comparison matrix summarizes the preferences of the plant manager.
Detroit Cleveland St. Louis
Detroit 1 1/3 1/4
Cleveland 3 1 1/2
St. Louis 4 2 1
Which choice does the decision maker prefer?
A) Detroit
B) Cleveland
C) St. Louis
D) Cleveland and St. Louis are equally preferred
E) Detroit and St. Louis are equally preferred
98) Three fast food restaurants on a college campus have been subjected to pairwise comparisons on the quality of their food. The matrix is
Pizza Mama’s Papa’s Freddie’s
Mama’s 1 3 8
Papa’s 1 4
Freddie’s 1
Which choice does the decision maker prefer?
A) Mama’s
B) Papa’s
C) Freddie’s
D) Mama’s and Papa’s are equally preferred.
E) Cannot be determined from the information provided
99) In the __________ process, the decision maker determines how well each alternative scores on a criterion using pairwise comparisons.
A) linear programming
B) simplex tableau
C) goal programming
D) analytical hierarchy
100) In the analytical hierarchy process, a high consistency ratio is considered __________ consistent than a low consistency ratio.
A) less
B) more
C) none of the above
101) A required step in the analytic hierarchy process is to determine the
A) number of hierarchies to use
B) relative importance of a set of features based on a criterion
C) goals to be satisfied
D) expected value of the criteria
102) An art critic is evaluating four different interpretations “The Nutcracker”. The pairwise comparison matrix for the criterion “originality of choreography” is given below.
Choreographer A B C D
A 1 1/3 3 4
B 3 1 5 2
C 1/3 1/5 1 6
D 1/4 1/2 1/6 1
Determine the priorities of the four choreographers relative to “originality”.
A) A is preferred to B; B is preferred to C; and C is preferred to D.
B) B is preferred to A; A is preferred to D; and D is preferred to C.
C) B is preferred to A; A is preferred to C; and C is preferred to D.
D) C is preferred to A; A is preferred to D; and D is preferred to B.
103) In synthesization, dividing each value in each column of the pairwise comparison matrix by the corresponding column sum, we obtain the __________ matrix.
A) pairwise
B) normalized
C) preference
D) criteria
E) criteria preference
104) Assume that a plant manager has to decide where to locate its warehouse The decision has been narrowed down to choices among the following three cities: Detroit, Michigan, Cleveland, Ohio and St. Louis Missouri. The company has weighted each of these criteria in terms of its relative importance in the decision making process, and it has analyzed each potential warehouse location and graded them according to each criteria as shown in the following table.
St. Louis
Proximity to suppliers .45 80 70 60
Proximity to customers .35 75 90 80
Land and construction costs .20 60 50 85
Calculate the scores for each location and state where the warehouse should be located?
A) Detroit
B) Cleveland
C) St. Louis
D) Cleveland and St. Louis are equally preferred
E) Detroit and St. Louis are equally preferred
105) A business is trying to decide which restaurant to hold its annual awards banquet. Use the information below to determine the best choice.
Restaurant
Criteria Weight A B C
Appearance 0.15 40 65 60
Service 0.30 75 80 70
Atmosphere 0.15 60 40 70
Location 0.10 90 100 75
Quality of food 0.30 70 80 75
Where should the restaurant be located?
A) A
B) B
C) C
D) A and B equally preferred
E) B and C equally preferred
Introduction to Management Science, 10e (Taylor)
Chapter 10 Nonlinear Programming

1) The slope of a curve at any point is equal to the derivative of the curves function.
2) The slope of a curve at its highest point equals 1.
3) Decision variables cannot be multiplied by each other in the objective function of a nonlinear program.
4) More attention has been devoted to linear programs than to non linear programs because these types of problems are more realistic in business.
5) Both linear and nonlinear programming models are examples of constrained optimization models.
6) An optimal solution to a nonlinear programming problem will always occur at the boundary of the feasible solution space formed by the constraint.
7) The Lagrange multiplier is analogous to the dual variables in a linear programming problem.
8) The Lagrange multiplier at the optimum gives only the instantaneous rate of change in the objective value.
9) Both linear and nonlinear programming models have the general form of an objective function subject to more than 1 constraint.
10) The classic optimization is the use of calculus to determine the optimal value of a variable.
11) If a nonlinear program has been correctly formulated, procedures guarantee a solution.
12) In an unconstrained nonlinear programming problem, we have a single nonlinear objective function and no constraints.
13) Constraints for nonlinear programs are usually nonlinear.
14) In portfolio selection problems, risk is measured by the variance of the return on the portfolio.
15) In solving the facility location problem, the objective is to locate a centralized facility that serves customers or other facilities such that the distance traveled between the facility and customers or other facilities is minimized.
16) If a nonlinear programming model consists of a single nonlinear objective function and a single linear constraint, it is called a(n) __________ optimization problem.
17) If a nonlinear programming model consists of a single nonlinear objective function and no constraints, it is called a(n) __________ optimization problem.
18) The __________ reflects the approximate change in the objective function resulting from a unit change in the quantity (right-hand-side) value of the constraint.
19) Assume a nonlinear programming problem with a single constraint has been solved. The value of the Lagrange multiplier is \$0.75 and the value of the optimal profit (Z) is \$25. If the right-hand-side of the constraint is increased from 38 to 42, the new value of Z will be __________.
20) If a nonlinear programming problem results in profit (Z) of \$50, and the Lagrange multiplier for a constraint is -2, the new profit will be __________ if the right hand side of the constraint is increased by 1 unit.
21) If a firm’s profit is Z = 100p -8p2 +16, then the maximum profit occurs where p = __________.
22) If a firm’s profit is z = 20p -2p2 + 40, then the optimal value of p yields a maximum profit of __________.
23) Assume price and demand are related by the following function: v = 200 – p. If fixed cost = \$10,000 and variable cost = \$8, then the expression for profit is __________.
24) Assume price and demand are related by the following function: v = 100 – 2.5p. If fixed cost = \$5,000 and variable cost = \$10, then the expression for profit is __________.
25) __________, a measure of correlation between returns on investment i and returns on investment j is used to reflect risk.
26) The __________ of the value of investment is a measure of risk.
27) The __________ measure of distance between two points on a set of X and Y coordinates is the hypotenuse of right triangle.
28) The objective of a facility location problem is to minimize __________.
The XYZ manufacturing company produces ball bearings. The annual fixed cost is \$20,000 and the variable cost per ball bearing is \$3. The price is related to demand according to the following equation: 1,000 – 8p.
29) What is the nonlinear profit function for the XYZ company? Simplify the terms as much as possible.
30) What is the derivative of the profit function for the XYZ company? Simplify the terms as much as possible.
31) What price for the ball bearings will maximize the profit?
32) What is the optimal production quantity?
33) What is the optimal profit?
34) Determine the quantity of soap and shampoo that should be produced to maximize profit.
35) Determine the profit for the optimal production quantities of soap and shampoo.
36) Lush Lawns, Inc. provides a lawn fertilizer and weed control service. They are adding a special aeration treatment as a low-cost extra service option, which it hopes will help attract new customers. Management is planning to promote this new service in two media: radio and direct-mail advertising. A budget of \$2000 is to be used on this promotional campaign over the next quarter. Based on past experience in promoting its other services, Lush Lawns has been able to obtain an estimate of the relationship between sales and the amount spent on promotion in these two media:
s = 2 X12 – 10 X22 – 2x1x2 + 18×1 + 34×2
s.t. x1 + x2 = 2
Solve.
37) Zoey’s Catnip Toys faces the following relationship between price and demand: v = 2000 – 200p. The fixed cost is \$500 and variable cost is \$1. Write an expression for the total profit.
38) Zoey’s Catnip Toys faces the following relationship between price and demand: v = 2000 – 200p. The fixed cost is \$500 and variable cost is \$1. What price should Zoey charge to maximize profit?
Sara’s Sensible Critters makes two kinds of catnip toys: balls (x1) and mice (x2). The relationship between demand and price for balls and mice is:
x1 = 1800 – 150p1
x2 = 1500 – 300p2
The cost for a catnip ball is \$2 and for the mouse, \$3.
Customer demand requires that she make 2.5 times more balls than mice.
39) Write the formulation for this problem
40) Determine the prices that Sara should charge to maximize profit
41) Sara has found an unlimited source of catnip so that is no longer a constraint. However, customer demand dictates that she produce 2.5 times more catnip balls than mice. Write the new constraint.
42) Sara has found an unlimited source of catnip so that is no longer a constraint. However, customer demand dictates that she produce 2.5 times more catnip balls than mice. How will this impact the prices that she should charge to maximize profit?
43) A store has determined that the weekly sales of a product is related to the number of customers who visit the store and the square feet of shelf space, x, according to the following equation: -20×2 – 10C2 + 40Cx + 120x – 200C + 600. C represents the hundreds of customers who visit their store. If a store averages 200 customers per week, how many square feet of shelf space is required to maximize sales?
44) The slope of a curve at its highest point equals
A) 0
B) 1
C) 2
D) 3
45) A store has determined that the weekly sales of a product is related to the number of customers who visit the store and the square feet of shelf space, x, according to the following equation: -20×2 – 10C2 40Cx + 120x – 200. C represents the hundreds of customers who visit their store. If a store averages 200 customers per week, how many square feet of shelf space is required to maximize sales?
A) 3
B) 4
C) 5
D) 1 or 9
E) None of the above
46) If a firm’s profit is Z = 12x -6×2 + 30, and their minimum production level of x is equal to 0.5, then the level of x that maximizes profit is
A) .5
B) 1
C) 1.5
D) 2
E) None of the above
47) A customer molder produces 6-ounce juice glasses and 10-ounce cocktail glasses. The per unit contribution for the juice glasses (x1) is equal to 60 – 5×1, and the per unit contribution for the cocktail glasses (x2) is 80 – 4×2. An expression for the total contribution is:
A) 20 – 4×2 – 5×1
B) 60×1 – 5 x12 + 80×2 – 4 x22
C) 80×1 – 5 x12 + 60×2 – 4 x22
D) 20 – (4×2)(5×1)
E) None of the above
48) Classical optimization is the use of __________ to determine the optimal value of a variable.
A) calculus
B) linear programming
C) nonlinear programming
D) goal programming
49) The derivative of a function __________ the slope of the curve defined by that function.
A) is larger than
B) equals
C) is smaller than
D) is similar to
50) Both linear and nonlinear programming models are examples of
A) goal programming models
B) simplex tableaus
C) constrained likelihood models
D) constrained optimization models
51) The Lagrange multiplier reflects the appropriate change in the objective function resulting from a unit change in the __________ of the constraint equation.
A) coefficient
B) objective function
C) right hand side
52) The Lagrange multiplier is __________ to the dual variables in a linear programming problem.
A) analogous
C) inversely related
D) opposite
53) The Lagrange multiplier
A) is the shadow price for the objective function coefficients
B) is not valid over a range of changes in the RHS
C) is the rate of change in the objective value as the RHS of the constraint increases
D) all of the above
54) The XYZ manufacturing company produces ball bearings. The annual fixed cost is \$20,000 and the variable cost per ball bearing is \$3. The price is related to demand according to the following equation: 1,000 – 8p. What is the optimal price of the ball bearings that will maximize the profit?
A) 47.99
B) 53.99
C) 58.99
D) 63.99
E) 67.99
55) The XYZ manufacturing company produces ball bearings. The annual fixed cost is \$20,000 and the variable cost per ball bearing is \$3. The price is related to demand according to the following equation: 1,000 – 8p. What is optimal profit?
A) \$5668
B) \$6668
C) \$7668
D) \$8668
E) \$9668
The Salt Creek soap company has determined the following nonlinear model to determine the optimal pounds of industrial soap (X1) and shampoo (X2) it should produce each day.
Maximize Z = X12 + 2 X22 – 8X1 – 12X2 + 34
Subject to: X1 + 2X2 = 4 lbs
56) What quantities of soap and shampoo maximize profit?
A) X1 = 2, X2 = 1
B) X1 = 1, X2 = 2
C) X1 = 3, X2 = 1
D) X1 = 2, X2 = 2
E) X1 = 2, X2 = 3
57) What is profit when the optimal values of soap and shampoo are produced?
A) Z = 10
B) Z = 11
C) Z = 12
D) Z = 13
E) Z = 14
Sara’s Sensible Critters makes two kinds of catnip toys: balls (x1) and mice (x2). The relationship between demand and price for balls and mice is:
x1 = 1800 – 150p1
x2 = 1500 – 300p2
The cost for a catnip ball is \$2 and for the mouse, \$3.
Customer demand requires that she make 2.5 times more balls than mice.
58) Write the appropriate expression for profit
A) Max Z = (p1 – 3)x1 + (p2 – 2)x2
B) Max Z = (p1 + 2)x1 + (p2 + 3)x2
C) Max Z = (p1 – 2)x1 + (p2 – 3)x2
D) Min Z = (p1 – 2)x1 + (p2 – 3)x2
E) None of the above are correct
59) Write the appropriate expression for the demand constraint.
A) 2.5×1 = x2
B) x1 – 2.5×2 ≥ 0
C) x1 + 2.5×2≤ 0
D) x1 = 2.5×2
E) None of the above are correct
Introduction to Management Science, 10e (Taylor)
Chapter 11 Probability and Statistics

1) Deterministic techniques assume that no uncertainty exists in model parameters.
2) Probabilistic techniques assume that no uncertainty exists in model parameters.
3) Objective probabilities that can be stated prior to the occurrence of an event are classical or a priori.
4) Objective probabilities that are stated after the outcomes of an event have been observed are relative frequencies.
5) Relative frequency is the more widely used definition of objective probability.
6) Subjective probability is an estimate based on personal belief, experience, or knowledge of a situation.
7) An experiment is an activity that results in one of several possible outcomes.
8) The events in an experiment are mutually exclusive if only one can occur at a time.
9) In a given experiment, the probabilities of all mutually exclusive events sum to one.
10) A set of events is collectively exhaustive when it includes all the events that can occur in an experiment.
11) A marginal probability is the probability of a single event occurring.
12) A Venn diagram visually displays mutually exclusive and non-mutually exclusive events.
13) A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously.
14) A conditional probability is the probability that an event occurs given that another event has already occurred.
15) Conditional probabilities are shown in Venn diagrams.
16) Probability trees are used only to compute conditional probabilities.
17) A succession of events that does not affect other events is independent.
18) A binomial probability distribution indicates the probability of r successes in n trials.
19) The chi-square test is a statistical test to determine if data that are squared exhibit bias.
20) A continuous random variable may assume only integer values within a given interval.
21) Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed.
22) Another name for the mean of a probability distribution is its expected value.
23) An inspector correctly identifies defective products 90% of the time. For the next 10 products, the probability that he makes fewer than 2 incorrect inspections is 0.736.
24) In Bayesian analysis, additional information is used to alter the conditional probability of the occurrence of an event.
25) Objective probabilities that can be stated prior to the occurrence of an event are __________.
26) __________ probability is an estimate based on a personal belief, experience, and knowledge of a situation.
27) The events in an experiment are __________ if only one can occur at a time.
28) A __________ organizes numerical data to describe the events of an experiment.
29) A __________ is the probability of occurrence of a single event.
30) __________ can enable one to improve marginal probabilities of the occurrence of an event by gathering additional information.
31) A succession of events that do not affect each other are __________.
32) A __________ probability is the probability that an event will occur given that another event has already occurred.
33) In a binomial distribution process, there are __________ possible outcomes.
34) One of the properties of the __________ distribution is that the probability of success remains constant over time.
35) Altered marginal probability of an event based on additional information is a __________ probability.
36) The __________ of a random variable is computed by multiplying each possible value of the variable by its probability and summing these products.
37) If events A and B are independent, then P(AB) = __________.
38) If events A and B are independent, then P(A|B) = __________.
39) If two events are not mutually exclusive, then P(A or B) = __________.
40) __________ is a measure of dispersion of random variable values about the expected value.
41) A continuous random variable can take on a(n) __________ number of values within a given interval.
42) The __________ test is a statistical test to see if an observed data fit a particular probability distribution.
43) The __________ normal distribution has a mean of 0 and a standard deviation of 1.
44) Almost all of the data from a normal distribution fall within __________ standard deviations of the mean.
45) The expected value of the standard normal distribution is equal to __________.
46) The standard deviation of the standard normal distribution is equal to __________.
Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y.
47) What is the probability that Jim will be accepted at both universities?
48) What is the probability that Jim will not be accepted at either university?
49) What is the probability that Jim will be accepted by at least one of the two universities?
Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category.
Male (M) Female (F)
Job
Salaried staff (SS) 30 50
Hourly staff (HS) 60 40
50) If an employee is selected at random, what is the probability that the employee is male?
51) If an employee is selected at random, what is the probability that the employee is male and salaried staff?
52) If an employee is selected at random, what is the probability that the employee is female given that the employee is a salaried staff member?
53) If an employee is selected at random, what is the probability that the employee is female or works as a member of the administration
An automotive center keeps tracks of customer complaints received each week. The probability distribution for complaints can be represented as a table or a graph, both shown below. The random variable xi represents the number of complaints, and p(xi) is the probability of receiving xi complaints.
xi 0 1 2 3 4 5 6
p(xi) .10 .15 .18 .20 .20 .10 .07
54) What is the probability that they receive less than 3 complaints in a week?
55) What is the average number of complaints received per week?
56) A fair die is rolled nine times. What is the probability that an odd number (1,3 or 5) will occur less than 3 times?
57) A fair die is rolled 8 times. What is the probability that an even number (2,4, 6) will occur between 2 and 4 times?
A company markets educational software products, and is ready to place three new products on the market. Past experience has shown that for this particular software, the chance of “success” is 80%. Assume that the probability of success is independent for each product.
58) Find the probability that exactly 1 of the 3 products is successful.
59) Find the probability that none of the 3 products is successful.
60) If X has the following probability distribution
X 1 2 3 4
P(X) .1 .5 .2 .2
Compute the expected value of X
61) If X has the following probability distribution
X 1 2 3 4
P(X) .1 .5 .2 .2
Compute the standard deviation of X.
62) If x is normally distributed with a mean of 10 and a standard deviation of 3, then P(x ≤ 6) is equal to P( Z ≤ __)?
63) For a standard normal distribution, what is the probability that z is greater than 1.75?
Two Psychology majors, in 2 different sections of Clinical Psychology, were comparing test scores. The following gives the students’ scores, class mean, and standard deviation for each section:
Section 1 Section 2
Student Score 84 75
Mean 75 60
Standard deviation 7 8
64) What is the z-score of the student from section 1 and what is the probability that a student in section 1 will score higher than 84?
65) What is the z-score of the student from section 2 and what is the probability that a student in section 2 will score higher than 75?
66) Which student scored better compared to the rest of the section?
67) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is larger than 21 oz?
68) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf of bread is larger than 23 oz?
69) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is less than 24 oz?
70) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is between 20.75 and 23.25 oz?
71) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is between 21.75 and 22.25 oz?
72) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is more than 24 oz?
73) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is more than 22.25 oz?
74) A life insurance company wants to estimate their annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the plan recipients would receive payments beyond age 75?
75) A life insurance company wants to estimate their annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the participants die before they reach the age of 65?
76) A life insurance company wants to estimate their annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. By what age have 80% of the plan participants pass away?
77) For the normal distribution, the mean plus and minus 1.96 standard deviations will include what percent of the observations?
78) What is the area under the normal curve for ≥ 1.79?
79) A study of a company’s practice regarding the payment of invoices revealed that on the average an invoice was paid 20 days after it was received. The standard deviation equaled 5 days. Assuming that the distribution is normal, what percent of the invoices is paid within 15 days of receipt?
80) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. Assuming the weights of the crab are normally distributed, what is the probability that a randomly selected crab will weigh more than 2 .2 pounds?
81) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. Assuming the weights of crab are normally distributed, what is the probability that a randomly selected crab will weigh between 1 and 2 pounds?
82) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. Assuming the weights of crab are normally distributed, the probability that a randomly selected crab will weigh less than 1.2 pounds is __________.
83) Assume that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2. Find the probability that X is between 48 and 55.
84) A paint manufacturer’s production process is normally distributed with a mean of 100,000 gallons and a standard deviation of 10,000 gallons. Management wants to create an incentive bonus for the production crew when the daily production exceeds the 94th percentile of the distribution. At what level of production should management pay the incentive bonus?
An online sweepstakes has the following payoffs and probabilities. Each person is limited to one entry.
85) The probability that someone wins any money is ________.
86) The probability of winning at least \$1,000.00 is ________.
87) __________ techniques assume that no uncertainty exists in model parameters.
A) Probability
B) Probabilistic
C) Deterministic
D) Distribution
88) __________ probability is an estimate based on personal belief, experience, or knowledge of a situation.
A) Binomial
B) Subjective
C) Marginal
D) Joint
89) Objective probabilities that can be stated prior to the occurrence of an event are
A) subjective
B) a priori
C) classical or a priori
D) none of the above
90) The events in an experiment are __________ if only one can occur at a time.
A) mutually exclusive
B) non-mutually exclusive
C) mutually inclusive
D) independent
91) In a given experiment the probabilities of mutually exclusive events sum to
A) 0
B) 0.5
C) 1
D) none of the above
92) A __________ probability is the probability of a single event occurring.
A) subjective
B) binomial
C) marginal
D) joint
93) A frequency distribution is an organization of __________ data about the events in an experiment.
A) quantitative
B) numerical
C) qualitative
D) A and B
94) P(A U B) is the probability that __________ will occur.
A) A
B) B
C) A and B
D) A or B or both
95) Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. What is the probability that Jim will be accepted at both universities?
A) .65
B) .25
C) .20
D) 09
E) .05
96) Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. What is the probability that Jim will not be accepted at either university?
A) .20
B) .30
C) .36
D) .44
E) 56
97) Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category.
Male (M) Female (F)
Job
Salaried staff (SS) 30 50
Hourly staff (HS) 60 40
If an employee is selected at random, what is the probability that the employee is female or works as a member of the administration
A) .1667
B) .60
C) .67
D) .70
E) .73
98) A __________ probability distribution indicates the probability of r successes in n trials.
A) joint
B) subjective
C) marginal
D) binomial
99) The probability of independent events occurring in succession is computed by __________ the probabilities of each event.
A) multiplying
C) subtracting
D) dividing
100) A __________ probability is the probability that an event will occur given that another event has already occurred.
A) subjective
B) objective
C) conditional
D) binomial
101) In Bayesian analysis, additional information is used to alter the __________ probability of the occurrence of an event.
A) marginal
B) conditional
C) binomial
D) revised
102) Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category.
Male (M) Female (F)
Job
Salaried staff (SS) 30 50
Hourly staff (HS) 60 40
If an employee is selected at random, what is the probability that the employee is female given that the employee is a salaried staff member.
A) .1667
B) .50
C) .60
D) .625
E) .70
103) A __________ probability is the altered marginal probability of an event based on additional information.
A) posterior
B) joint
C) marginal
D) conditional
E) A and B
104) Mutually exclusive events are
A) events with identical probabilities
B) events that have no outcomes in common
C) events that have no effect on each other
D) all of the above
105) Bayesian analysis involves a(n) __________ probability.
A) a priori
B) posterior
C) joint
D) relative frequency
106) In a __________ distribution, for each of n trials, the event always has the same probability of occurring.
A) binomial
B) joint
C) frequency
D) standard
107) Experiments with repeated independent trials will be described by the binomial distribution if
A) each trial result influences the next
B) each trial has exactly 2 outcomes whose probabilities do not change
C) the trials are continuous
D) the time between trials is constant
108) In a binomial distribution, for each of n trials, the event
A) time between trials is constant
B) always has the same probability of occurring
C) result of the first trial influence the next trial
D) trials are continuous
109) A fair die is rolled nine times. What is the probability that an odd number (1,3 or 5) will occur less than 3 times?
A) .0899
B) .2544
C) .7456
D) .9101
E) .9916
110) A fair die is rolled 8 times. What is the probability that an even number (2,4, 6) will occur between 2 and 4 times?
A) .1640
B) .2188
C) .4922
D) .6016
E) .8204
111) A company markets educational software products, and is ready to place three new products on the market. Past experience has shown that for this particular software, the chance of “success” is 80%. Assume that the probability of success is independent for each product. What is the probability that exactly 1 of the 3 products is successful?
A) 0.80
B) 2.4
C) 0.032
D) 0.24
E) 0.096
112) __________ is a measure of the dispersion of random variable values about the expected value or mean.
A) Standard deviation
B) Sample mean
C) Population mean
D) Variance
E) A and D
113) An automotive center keeps tracks of customer complaints received each week. The probability distribution for complaints can be represented as a table or a graph, both shown below. The random variable xi represents the number of complaints, and p(xi) is the probability of receiving xi complaints.
xi 0 1 2 3 4 5 6
p(xi) .10 .15 .18 .20 .20 .10 .07
What is the average number of complaints received per week?
A) 2.12
B) 3.32
C) 4.12
D) 2.83
E) None of the above
114) The expected value of the standard normal distribution is equal to
A) 0
B) 1
C) 1.5
D) 2
E) 2.5
115) The area under the normal curve represents probability, and the total area under the curve sums to
A) 0
B) 0.5
C) 1
D) 2
116) The __________ and variance are derived from a subset of the population data and are used to make inferences about the population.
A) Population variance
B) Population standard deviation
C) population mean
D) sample mean
E) sample range
117) Under the normal curve, the area between z=1 and z =-2 includes approximately __________ of the values.
A) 99%
B) 98%
C) 95%
D) 85%
E) 82%
118) For the normal distribution, the mean plus and minus 1.96 standard deviations will include what percent of the observations?
A) 80%
B) 84%
C) 90%
D) 95%
E) 97%
119) A jar of jelly is normally distributed with a mean of 16 oz and a standard deviation of 0.02 oz. What is the probability that a jar of jelly contains less than 16 oz?
A) .1915
B) .3085
C) .5000
D) .7257
E) .8413
120) A jar of jelly is normally distributed with a mean of 16 oz and a standard deviation of 0.02 oz. What is the probability that a jar of jelly contains more than 16.03 oz?
A) .0668
B) .1587
C) .3413
D) .4332
E) .9332
121) Under the normal curve, the area between z=2 and z =-2 includes __________ of the values.
A) 98%
B) 96%
C) 95%
D) 93%
E) 90%
122) The metropolitan airport commission is considering the establishment of limitations on noise pollution around a local airport. At the present time, the noise level per jet takeoff in one neighborhood near the airport is approximately normally distributed with a mean of 100 decibels and a standard deviation of 3 decibels. What is the probability that a randomly selected jet will generate a noise level of more than 105 decibels?
A) 0.0228
B) 0.0475
C) 0.0485
D) 0.0500
E) None of the above
123) For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.2910. The value of Z is:
A) 0.17
B) 0.81
C) 1.25
D) 1.65
124) For some value of Z, the probability that a standard normal variable is below Z is 0.3783. The value of Z is:
A) -0.81
B) -0.31
C) 0.82
D) 1.55
125) For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3554. The value of Z is:
A) 0.31
B) 0.36
C) 0.95
D) 1.06
126) If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.
A) 0.3551
B) 0.3085
C) 0.2674
D) 0.1915
127) Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. Find the probability that a randomly selected college student will take between 2 and 6 minutes to find a parking spot in the main parking lot.
A) 0.1950
B) 0.4772
C) 0.4332
D) 0.6247
128) Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. What time is exceeded by approximately 75% of the college students when trying to find a parking spot in the main parking lot?
A) 3.5 minutes
B) 5.75 minutes
C) 6.36 minutes
D) 9.2 minutes
129) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. What weight is exceeded by 2% of all of the crabs? (Assume the weights are normally distributed.)
A) 0.78 pounds
B) 1.82 pounds
C) 2.42 pounds
D) 4.36 pounds
130) A professor would like to assign grades such that 5% of students receive As. If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an A? (Round your answer.)
A) 80
B) 83
C) 90
D) 93
131) A professor would like to assign grades such that 7% of students receive Fs. If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an F? (Round your answer.)
A) 43
B) 49
C) 50
D) 55
Introduction to Management Science, 10e (Taylor)
Chapter 12 Decision Analysis

1) A state of nature is an actual event that may occur in the future.
2) A payoff table is a means of organizing a decision situation, including the payoffs from different decisions given the various states of nature.
3) The maximax criterion results in the maximum of the maximum payoffs.
4) The maximin approach involves choosing the alternative with the highest payoff.
5) Regret is the difference between the payoff from the best decision and all other decision payoffs.
6) The minimax regret criterion minimizes the maximum regret.
7) The minimax regret criterion maximizes the maximum regret.
8) The Hurwicz criterion is a compromise between the maximax and maximin criteria.
9) The Hurwicz criterion is a compromise between the minimax and minimin criteria.
10) The coefficient of optimism is a measure of the decision maker’s optimism.
11) The Hurwicz criterion multiplies the best payoff by the coefficient of optimism.
12) The Hurwicz criterion multiplies the worst payoff by the coefficient of optimism.
13) A dominant decision is one that has better payoff than another decision under each state of nature.
14) The appropriate criterion is dependent on the risk personality and philosophy of the decision maker.
15) The maximax criterion is optimistic.
16) The maximin criterion maximizes the minimum regret.
17) The minimax criterion minimizes the maximum payoff.
Diff: 1 Page Ref: 531
Main Heading: Decision Making without Probabilities
Key words: minimax criterion
18) Regret and opportunity loss mean the same thing.
19) The equal likelihood criterion assigns a probability of 0.5 to each state of nature.
20) Expected opportunity loss is the expected value of the regret for each decision.
21) When using decision trees, branches with the greatest expected value are selected.
22) A decision tree is a diagram consisting of circles decision nodes, square probability nodes, and branches.
23) When the __________ criterion is used, the maximum of the maximum payoffs is observed.
24) When the __________ criterion is used, the maximum of the minimum payoffs is observed
25) __________ is the difference between the payoff from the best decision and all other decision payoffs.
26) The __________ is a compromise between the maximax and the maximin criterion.
27) The __________ is a measure of the decision makers optimism.
28) A(n) __________ decision is one that has a better payoff than another decision under the state of nature.
29) A __________ structures decisions with series of nodes.
30) The __________ of sample information is the ratio of the expected value of sample information to the expected value of perfect information.
31) When the __________ criterion is used, the decision maker selects the decision alternative that minimizes the maximum regret.
32) A ________ decision tree illustrates a situation requiring a services of decisions.
33) ________ is a measure of personal satisfaction derived from money.
34) People who forgo a high expected value to avoid a disaster with a low probability are __________.
A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.
Weather
Cold Warm Rainy
S1 S2 S3
Bike: A1 10 8 6
Hike: A2 14 15 2
Fish: A3 7 8 9
35) If the group is optimistic, what decision should they make?
36) If the group is conservative, what decision will they make?
37) If the group chooses to minimize their maximum regret, what activity will they choose?
38) If the probabilities of cold weather (S1), warm weather (S2), and rainy weather (S3) are 0.2, 0.4, and 0.4, respectively, then what decision should be made using the expected value criterion?
39) What is the EVPI for this situation?
An investor is consider 4 different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below.
Economic Condition
Poor Average Good Excellent
Investment (S1) (S2) (S3) (S4)
A 50 75 20 30
B 80 15 40 50
C -100 300 -50 10
D 25 25 25 25
40) What decision would be made under maximax?
41) What decision would be made under maximin?
42) What decision would be made under minimax regret?
43) If the probabilities of each economic condition are 0.5, 0.1, 0.35, and 0.05 respectively, what investment would be made using the expected value criterion?
44) What is the expected value of perfect information?
A manager has developed a payoff table that indicates the profits associated with a set of alternatives under 2 possible states of nature.
Alt S1 S2
1 10 2
2 -2 8
3 8 5
45) If the manager uses maximin as the decision criterion, which of the alternatives should she choose?
46) If the manager uses minimax regret as the decision criterion, which of the alternatives would she choose?
47) Use the expected value criterion to select the best alternative. Assume that the probability of S2 is equal to 0.4.
48) Compute the expected value of perfect information assuming that the probability of S2 is equal to 0.4.
The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code.
49) If he uses the maximin criterion, how many new workers will he hire?
50) If he uses the minimax regret criterion, how many new workers will he hire?
51) If he thinks the chances of low, medium, and high compliance are 20%, 30%, and 50% respectively, what are the expected net revenues for the number of workers he will decide to hire?
52) If he thinks the chances of low, medium, and high compliance are 20%, 30%, and 50% respectively, what is the expected value of perfect information?
A manufacturer must decide whether to build a small or a large plant at a new location. Demand at the location can be either small or large, with probabilities estimated to be 0.4 and 0.6 respectively. If a small plant is built, and demand is large, the production manager may choose to maintain the current size or to expand. The net present value of profits is \$223,000 if the firm chooses not to expand. However, if the firm chooses to expand, there is a 50% chance that the net present value of the returns will be 330,000 and 50% chance the estimated net present value of profits will be \$210,000. If a small facility is built and demand is small, there is no reason to expand and the net present value of the profits is \$200,000. However, if a large facility is built and the demand and the demand turns out to be small, the choice is to do nothing with a net present value of \$40,000 or to stimulate demand through local advertising. The response to advertising can be either modest with a probability of .3 or favorable with a probability of .7. If the response to advertising is modest the net present value of the profits is \$20,000. However, if the response to advertising is favorable, then the net present value of the profits is\$220,000. Finally, the when large plant is built and the demand happens to be high, the net present value of the profits \$800,000.
53) Draw a decision tree.
54) Draw a decision tree and determine the payoff for each decision and event node. Which alternative should the manufacturer choose?
55) If a student attends every management science class, the probability of passing the course is 0.80; but if the student only attends randomly, then the probability of passing the course is 0.50. If a student fails, they can take a makeup exam where the probability of passing is 0.60 if the student has attended every class. This probability of passing the makeup exam drops to 0.10 if the student has attended at random.
Passing the course is worth 5 credits. Full time attendance “costs” 3 credits in terms of energy and time whereas random attendance “costs” only 1 credit.
Use a decision tree to decide which is the best attendance pattern to adopt. Assume that all failing students take the make up exam and that the payoff for failing is equal to 0.
The quality control manager for ENTA Inc. must decide whether to accept (a1), further analyze (a2) or reject (a3) a lot of incoming material. Assume the following payoff table is available. Historical data indicates that there is 30% chance that the lot is poor quality (s1), 50 % chance that the lot is fair quality (s2) and 20% chance that the lot is good quality (s3).
56) What action would you choose according to maximax criterion?
57) What action would you choose according to maximin criterion?
58) Construct the regret table
59) What action would you choose according to minimax regret criterion?
60) What action would you choose according to expected value criterion?
61) What is the maximum amount that you would be willing to pay for perfect information?
62) Lucky Lucy is playing the slots in Reno, Nevada, holding her last silver dollar. There are three possible payoffs if she wins: one cherry, \$1.00; two cherries, \$5.00; or three cherries, \$50.00. Anything else on the slot machine loses.
Construct the payoff table for Lucky Lucy
63) Consider the following decision tree.
What is the expected value at node 4? 64) Consider the following decision tree.
What is the value associated with node 3?
Which decision, A or B, is best? What is the expected value of this decision?
66) The maximax criterion results in the
A) maximum of the minimum payoffs
B) maximum of the maximum payoffs
C) minimum of the maximum payoffs
D) minimum of the minimum payoffs
67) The maximin criterion results in the
A) minimum of the maximum payoffs
B) maximum of the maximum payoffs
C) maximum of the minimum payoffs
D) minimum of the minimum payoffs
68) Regret is the difference between the payoff from the
A) best decision and all other decision payoffs
B) worst decision and all other decision payoffs
C) best decision and the worst decision payoffs
D) none of the above
69) The __________ minimizes the maximum regret.
A) maximax regret criterion
B) minimax regret criterion
C) minimin regret criterion
D) maximin regret criterion
70) The minimax regret criterion
A) maximizes the minimum regret
B) minimizes the minimum regret
C) minimizes the maximum regret
D) maximizes the maximum regret
71) Determining the worst payoff for each alternative and choosing the alternative with the best worst is called
A) maximin
B) minimin
C) maximax
D) minimax
72) The maximin approach to decision making refers to
A) minimizing the maximum return
B) maximizing the minimum return
C) maximizing the maximum return
D) minimizing the minimum return
73) The term opportunity loss is most closely related to
A) maximin regret
B) maximax regret
C) minimax regret
D) minimin regret
74) The Hurwicz criterion is a compromise
A) for the maximin criterion
B) for the maximax criterion
C) between the maximax and maximin criteria
D) none of the above
75) The Hurwicz criterion multiplies the
A) best payoff by the coefficient of optimism
B) worst payoff by the coefficient of optimism
C) best payoff by the worst payoff
D) none of the above
76) The basic decision environment categories are
A) certainty
B) risk
C) uncertainty
D) all of the above
Diff: 2 Page Ref: 527
Main Heading: Decision Making without Probabilities
Key words: decision making
77) The basic decision environment categories are
A) certainty and risk
B) risk and uncertainty
C) certainty and uncertainty
D) certainty, uncertainty and risk
78) The Hurwicz criterion
A) multiplies the worst payoff by one minus the coefficient of optimism
B) multiplies the best payoff by the coefficient of optimism
C) is a compromise between the maximax and maximin criteria
D) all of the above
79) The appropriate criterion is dependent on
A) the risk personality of the decision maker
B) the philosophy of the decision maker
C) all of the above
D) none of the above
80) The __________ is a measure of the decision maker’s optimism.
A) equal likelihood criterion
B) dominant decision
C) coefficient of optimism
D) none of the above
81) The __________ multiplies the decision payoff for each state of nature by an equal weight.
A) dominant decision
B) coefficient of optimism
C) equal likelihood criterion
D) none of the above
82) A __________ is one that has better payoff than another decision under each state of nature.
A) coefficient of optimism
B) equal likelihood criterion
C) dominant decision
D) none of the above
83) A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.
The maximax strategy is:
B) Rent
C) Lease
D) Brisk
E) Slow
84) A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.
The maximin strategy is:
B) Rent
C) Lease
D) Brisk.
E) Slow
85) A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.
The equal likelihood criterion strategy is:
B) Rent
C) Lease
D) High
E) Low
86) A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.
If the probability of brisk business is .40 and for slow business is .60, the expected value of perfect information is:
A) 12
B) 55
C) 57
D) 69
E) 90
87) The __________ is computed by multiplying each decision outcome under each state of nature by the probability of its occurrence.
A) expected value
B) expected value of perfect information
C) expected opportunity loss
D) none of the above
88) The __________ is the expected value of the regret for each decision.
A) expected value
B) expected opportunity loss
C) expected value of perfect information
D) none of the above
89) A tabular presentation that shows the outcome for each decision alternative under the various possible states of nature is called a
A) decision tree
B) payoff table
C) feasible region
D) payback matrix
90) The __________ is the maximum amount a decision maker would pay for additional information.
A) expected opportunity loss
B) expected value
C) expected value of perfect information
D) none of the above
91) A decision tree is a diagram consisting of
A) square decision nodes
B) circle probability nodes
C) branches representing decision alternatives
D) all of the above
92) In __________ additional information is used to alter the marginal probability of the occurrence of an event.
A) Bayesian analysis
B) decision analysis
C) probability analysis
D) all of the above
93) A __________ probability is the probability that an event will occur given that another event has already occurred.
A) posterior
B) conditional
C) marginal
D) all of the above
94) A __________ probability is the altered marginal probability of an event based on additional information.
A) marginal
B) conditional
C) posterior
D) none of the above
95) The efficiency of sample information is the ratio of the expected value of sample information to the
A) expected value of perfect information
B) expected value
C) utilization rate
D) coefficient of optimism
E) expected opportunity loss
96) The expected value of sample information
A) is never more than EVPI
B) can be compared to the sample cost to judge whether to sample.
C) is never negative
D) all of the above are true
E) Only A and C are true.
97) People who forgo a high expected value to avoid a disaster with a low probability are
A) risk takers
B) risk averters
C) risk calculators
D) risk predictors
98) People who take a chance on a bonanza with a very low probability of occurrence in lieu of a sure thing are
A) risk takers
B) risk averters
C) risk calculators
D) risk predictors
99) Utiles are units of __________ measures of utility.
A) quantitative
B) objective
C) subjective
D) qualitative
A small entrepreneurial company is trying to decide between developing two different products that they believe they can sell to two potential companies, one large and one small. If they develop Product A, they have a 50% chance of selling it to the large company with annual purchases of about 20,000 units. If the large company won’t purchase it, then they think they have an 80% chance of placing it with a smaller company, with sales of 15,000 units. On the other hand if they develop Product B, they feel they have a 40% chance of selling it to the large company, resulting in annual sales of about 17,000 units. If the large company doesn’t buy it, they have a 50% chance of selling it to the small company with sales of 20,000 units.
100) What is the probability that Product Awill being purchased by the smaller company?
A) 0.8
B) 0.5
C) 0.4
D) 0.2
E) 0.1
101) What is the probability that Product B will being purchased by the smaller company?
A) 0.8
B) 0.5
C) 0.4
D) 0.3
E) 0.1
102) How many units of Product A can they expect to sell?
A) 20,000
B) 17,000
C) 15,500
D) 15,000
E) 13,100
103) How many units of Product A can they expect to sell?
A) 20,000
B) 17,000
C) 15,500
D) 15,000
E) 13,100
104) How many units can they expect to sell for the optimum alternative?
A) 20,000
B) 17,000
C) 15,500
D) 15,000
E) 13,100
Introduction to Management Science, 10e (Taylor)
Chapter 13 Queuing Analysis

1) Providing quick service is an important aspect of quality customer service.
2) Operating characteristics describe the methods used by the service process.
3) Waiting lines form because people or things arrive at the servicing function, or server, faster than they can be served.
4) Components of a waiting line system include arrivals, servers, and the calling population.
5) The most important factors to consider in analyzing a queuing system are queuing discipline, arrival and service rate, and the nature of the calling population.
6) The queue discipline is the order in which waiting customers are served.
7) The calling population is the source of customers.
8) Calling populations are always finite.
9) The arrival rate is the frequency at which customers arrive at a waiting line according to a probability distribution.
10) The arrival rate is most frequently described by negative exponential distribution.
11) The service rate is the average time it takes to serve a customer.
12) The service time can often be described by the Poisson distribution.
13) Queuing system operating statistics are constant over time.
14) As the level of service improves, the cost of service decreases.
15) Queue discipline describes customers’ behavior in the queue.
16) The basic single server queuing model assumes an infinite calling population.
17) Utilization of 100% is necessary for a queuing system to reach a steady state.
18) Queuing models provide optimal solutions to waiting line problems
19) All single-server queuing models require the utilization factor to be less than 1.
20) Queue discipline refers to the willingness of customers to wait in line for service.
21) The basic single server model assumes that arrival rates are normally distributed.
22) A car wash with two attendants who work together as a team would be an example of a multiple-server system.
23) In multiple server models, two or more servers work as a team to serve a single waiting line.
24) In systems with finite queue length, the service rate does not have to exceed toe arrival rate.
25) The basic single server model assumes that customers who arrive first are served first.
26) If it takes 5 minutes to serve a customer at a fast food restaurant the service rate is _________.
27) The __________ is the average number of customers who can be served during a given time period.
28) The service time can most often be described by the __________ distribution.
Diff: 2 Page Ref: 590
Key words: service time, negative exponential distribution
29) The __________ is the frequency at which the customers arrive at a waiting line according to a probability distribution.
30) The arrival rate can generally be described by a(n) __________ distribution.
31) The __________ is the source of the customers or objects being simulated.
32) A system has one service facility that can service 10 customers per hour. The customers arrive at an average rate of 6 per hour. Utilization is __________.
33) A situation in which a mechanic is responsible for repairing a pool of fleet vehicles should be analyzed for a waiting line system with a __________ calling population
34) Customers arrive at a candy shop every 8 minutes on average. The arrival rate is __________.
35) If λ = 24 and μ = 30, then utilization is equal to __________.
36) If λ = 24 and μ = 30, then L is equal to __________.
37) If λ = 24 and μ = 30, then W is equal to __________ minutes.
38) If the __________ queuing system, which is a variation of the single phase single channel model, the service rate does not have to exceed the arrival rate.
39) A single channel queuing system has an average service time of 10 minutes and an average time between arrivals of 15 minutes. What is the arrival rate?
40) In a single server queuing system, if 10 customers arrive per hour, and 20 customers are served per hour, what is the probability that there are no customers in the system?
41) A single bay car wash with a Poisson arrival rate and an exponential service time has cars arriving an average of 15 minutes apart. It takes approximately 9 minutes to wash a car. What is the system utilization?
A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day.
42) What is the utilization rate for the mechanic?
43) What is the average time that a snowplow is out of service?
44) On average, how long does a snow plow wait before the mechanic can begin his repair?
45) Approximately how many vehicles are in the garage, waiting for or being repaired?
46) Poultry Processing processes chickens for fast food restaurants. The chickens arrive from the farms on trucks, in cages, at a rate of 8 trucks per hour according to the Poisson distribution. The quality standards of Poultry Processing require that the chickens be processes within 30 minutes, which includes the time from when the trucks arrive until the chickens are finished processing. Determine the maximum average processing rate (in truckloads per hour) that must be designed for the machine, in order to ensure that the cages will be processed, on the average, in 30 minutes or less. Assume processing time is exponentially distributed.
Lenny, a graduate research assistant “moonlights” at the short order counter in the student union snack bar in the evenings. He is the only one on duty at the counter during the hours he works. Arrivals to the counter seem to follow the Poisson distribution with a mean of 8 per hour. Each customer is served one at a time and the service time follows an exponential distribution with a mean of 5 minutes.
47) How long will a student wait in line, on average?
48) The manager thinks that students will go elsewhere for lunch if they have to wait more than 5 minutes. Therefore he’s thinking of hiring another server to help Lenny, reducing the customer service time to 4 minutes. How long will students wait in line if Lenny gets help?
49) Instead of having another student helps Lenny the manager is thinking of having two lines instead. Customers will equally divide themselves between the two lines. How long will students wait in line if there’s a second server? (Assume that the service time is 5 minutes.)
50) A hotel is considering changing its waiting line system. In the current system hotel guests divide themselves equally between the lines that form in front of 4 hotel clerks. The manager is considering having hotel guests wait in one line and then proceeding to the next available clerk. If average service time is 10 minutes and the average number of arrivals per hour is 12 guests, determine which system results in the lowest customer waiting time.
51) The local grocery store consists of two cashiers. The customers arrive according to Poisson distribution and the service times are based on negative exponential distribution. The average customer service time is five minutes and the average time between the arrivals of successive customers is 3 minutes. What is the probability that there are no customers in the grocery store?
The local grocery store consists of two cashiers. The customers arrive at the checkout according to the Poisson distribution and the service times are based on negative exponential distribution. The average customer service time is 4 minutes and the average time between the arrivals of successive customers is 3 minutes. Assume that customers equally divide themselves between the two cashiers.
52) What is the average number of customers waiting in each line and being checked out?
53) How much time is a customer expected to spend waiting in line and being checked out?
54) On average, how much time will the customer spend in line waiting to be served?
55) On the average, how many customers are waiting in line to be served?
56) A queuing system has 3 crews with 2 members each. What is the number of servers?
57) A multiple channel queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 6 customers per hour and an average service time of 20 minutes per customer. What is the minimum number of servers required to avoid an overloaded system?
In a factory machines breakdown at an average of 6 machines per hour according to a Poisson distribution. The time a repair person takes to repair the machine is not defined by any probability distribution but has a mean of 8 minutes and a standard deviation of 3 minutes.
58) What is the probability that no machine is being fixed?
59) On the average how many machines are waiting in line to be fixed?
60) On the average, how many machines are in the system either being repaired or waiting in line to be repaired?
61) On the average, how long will a machine have to wait before it is fixed?
62) On the average, how long will a machine be down and out of service?
In a bank drive-through, there is a single service window and room only for 2 cars to line-up to wait for service. The mean time between arrivals for drive through customers is five minutes. The mean time to complete a customer transaction is 3 minutes. The number of arrivals is distributed according to Poisson distribution and the service times are exponentially distributed.
63) What is the probability that there are no vehicles in the system?
64) On the average how many cars are in the system?
65) What is the probability that the system is full and the customer must drive on?
66) On the average, how many customers are waiting to be served?
67) What is the average time a customer spends in the system?
Diff: 3 Page Ref: 601
Key words: the avg time customer spends in system, finite queue length
68) What is the average time a customer spends in the line waiting to be served?
69) Operating characteristics for a waiting line system include
A) queue discipline
B) the Poisson distribution
C) a waiting line structure
D) utilization
70) The most important factors to consider in analyzing a queuing system are
A) the queue discipline
B) the queue structure
C) the queue order
D) all of the above
71) Customers may be served
A) according to a number assigned to each item
B) on a first-come-first serve basis
C) on a last-come-first-serve basis
D) all of the above
72) In a single-server queuing model, L represents
A) the length of time a customer waits
B) the size of the queue
C) the average number of customers in the queuing system
D) the length of the line
73) Operating characteristics
A) are averages
B) are constant over time
D) all of the above
74) Queuing discipline refers to the
A) reason waiting occurs in underloaded systems
B) willingness of customers to wait in line
C) order in which customers are processed
D) all of the above
75) The arrival rate is the
A) time between arrivals to the service facility
B) rate items arrive at the server after being in queue
C) rate of arrivals to the service facility
D) all of the above
76) A single server queuing system has average time between arrivals of 20 minutes and a service time of 10 minutes each. Assuming Poisson arrivals and exponential service times, the utilization factor is approximately
A) 0.25
B) 0.33
C) 0.50
D) 0.67
E) 2.0
77) What happens to the customer waiting time if system utilization increases?
A) decreases exponentially
B) decreases proportionally
C) increases proportionally
D) increases exponentially
78) What is not considered a measure of system performance in a queuing analysis?
A) average number in the system
B) system utilization
C) average number waiting in line
D) service time
79) Which of the following will not decrease system utilization?
A) increase in arrival rate
B) increase in service rate
C) increase in the number of servers
D) decrease in service time
A single server waiting line system has an arrival pattern characterized by a Poisson distribution with 3 customers per hour. The average service time is 12 minutes. The service times are distributed according to the negative exponential distribution.
80) The average time a customer can expect to wait in line is:
A) 18 minutes
B) 36 minutes
C) 30 minutes
D) 60 minutes
E) 72 minutes
81) The probability that the system is idle is:
A) 0
B) .20
C) .40
D) .60
E) .80
82) The expected number of customers in the system is:
A) 3.0
B) 1.5
C) 1.0
D) .90
E) .60
83) The expected number of customers in the waiting line is:
A) .6
B) .7
C) .8
D) .9
E) 1.0
84) A system has 5 servers. Customers arrive at a rate of 6 per hour and service time is 20 minutes. What is the system utilization?
A) .83
B) .40
C) .50
D) 20
A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day.
85) The utilization is
A) .30
B) .45
C) .57
D) .85
E) 1.00
86) Determine the average time that a snowplow is out of service.
A) .33 hours
B) 20 minutes
C) 2.64 hours
D) .33 days
E) 1.15 hours
87) On average, how long does a plow wait before the mechanic begins the repair?
A) 1 hour
B) 1.25 hours
C) 1.52 hours
D) 2 hours
E) 2.64 hours
88) What is the expected average number of snowplow in the garage (waiting for repair and being repaired)?
A) 1
B) 1.33
C) 2
D) 2.52
89) In a single server queuing system, if 12 customers arrive per hour, and 30 customers are served per hour, what is the probability that there are no customers in the system?
A) 0.75
B) 0.60
C) 0.40
D) 0.2 5
90) A manager is trying to improve a single-server queueing system through automation. The average service time is 20 minutes per customer, exponentially distributed, and the arrival rate is 16 customers per 8-hour day (Poisson arrivals). The automated system will have a constant service time of 16 minutes. The effect of this change will:
A) decrease utilization
B) increase waiting time
C) decrease waiting time
D) have no effect since the service time is unchanged
91) A multiple channel system has customers arriving at an average rate of 5 per hour and an average service time of 40 minutes. What minimum number of servers is required to ensure that the system is not overloaded?
A) 4
B) 5
C) 6
D) 3
92) A single channel queuing system has an average service time of 8 minutes and an average time between arrivals of 10 minutes. What is the hourly arrival rate?
A) 8
B) 6
C) 4
D) 2
93) A queuing system has 5 crews with 2 members each. What is the number of servers?
A) 2
B) 5
C) 10
D) none of the above
94) A multiple channel queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 4 customers per hour and an average service time of 18 minutes per customer. What is the minimum number of servers required to avoid an overloaded system?
A) 1
B) 2
C) 3
D) 4
95) Poultry Processing processes chickens for fast food restaurants. The chickens arrive from the farms on trucks, in cages, at a rate of 8 trucks per hour according to the Poisson distribution. The quality standards of Poultry Processing require that the chickens be processes within 30 minutes, which includes the time from when the trucks arrive until the chickens are finished processing. What is the maximum average processing rate (in truckloads per hour) that must be designed for the machine, in order to ensure that the cages will be processed, on the average, in 30 minutes or less. Assume processing time is exponentially distributed.
A) 4.5 trucks per hour
B) 9 trucks per hour
C) 10 trucks per hour
D) 18 trucks per hour
96) Constant service times occur with
A) machinery
B) well-trained employees
C) service processes
D) assembly processes
97) Customers arrive at a music store at an average of 1 per minute (Poisson arrivals). The service rate is 15 customers per hour (exponential service times). What is the minimum number of servers needed to keep the waiting time in the system under 5 minutes?
A) 4
B) 5
C) 6
D) 7
98) A single bay car wash with a Poisson arrival rate and an exponential service time has cars arriving on average of 10 minutes apart and an average service time of 4 minutes. What is the system utilization?
A) 0.2
B) 0.3
C) 0.4
D) 0.5
E) 0.6
99) Cars arrive at a single bay car wash on the average of 6 per hour according to the Poisson distribution. The wash time is a constant 4 minutes. What is the average number of cars in line?
A) .022
B) .133
C) .267
D) .667
100) Cars arrive at a single bay car wash on the average of 6 per hour according to the Poisson distribution. The wash time averages 4 minutes with a standard deviation of 1 minute, but the wash time is not defined by any distribution. What is the average number of cars in line?
A) .142
B) .267
C) .283
D) 2.83
E) 3.33
101) In a finite queue, the length of the queue is
A) limited
B) unlimited
C) limited or unlimited
D) limited and unlimited
102) Pickmeup is a drive through coffee house that has room for 3 cars in the driveway. The line cannot exceed 3 cars, and because they are exclusively drive through, customers may be turned away. In the morning, the arrival rate is 40 cars per hour (Poisson distributed) and with the servers working in teams, they can process 50 cars per hour (The service rate is exponential). What is the probability of turning customers away?
A) .173
B) .210
C) .339
D) .410
103) In multiple-server models, __________ independent servers in parallel serve a single waiting line.
A) 2 or more
B) 3 or more
C) 4 or more
D) 5 or more
The local grocery store consists of two cashiers. The customers arrive at the checkout according to the Poisson distribution and the service times are based on negative exponential distribution. The average customer service time is 4 minutes and the average time between the arrivals of successive customers is 3 minutes. Assume that customers equally divide themselves between the two cashiers.
104) How much time is a customer expected to spend in line at the checkout?
A) 11.2 minutes
B) 13.6 minutes
C) 14.4 minutes
D) 16.2 minutes
E) 18.2 minutes
105) On the average, how much time will the customer spend in line waiting to be served?
A) 11.2 minutes
B) 13.6 minutes
C) 14.4 minutes
D) 16.2 minutes
E) 18.2 minutes
106) What is the probability that there are no customers in the grocery store?
A) .0809
B) .0909
C) .10909
D) .1209
E) .1409
Introduction to Management Science, 10e (Taylor)
Chapter 14 Simulation

1) In computer mathematical simulation, a system is replicated with a mathematical model that is analyzed with the computer.
2) Monte Carlo is a technique for selecting numbers randomly from a probability distribution.
3) The Monte Carlo process is analogous to gambling devices.
4) In the Monte Carlo process, values for a random variable are generated by sampling from a probability distribution.
5) A long period of real time can be represented by a short period of simulated time.
6) Random numbers are equally likely to occur.
7) Simulation results will always equal analytical results if 30 trials of the simulation have been conducted.
8) It’s often difficult to validate that the results of a simulation truly replicate reality.
9) Simulation applies mathematical models to determine optimal solutions to business problems.
10) Validation of a simulation model occurs when the true steady state average results have been reached.
11) Random numbers generated by a mathematical process instead of a physical process are pseudorandom numbers.
12) Random numbers are typically generated on the computer using a numerical technique.
13) A table of random numbers must be normally distributed and efficiently generated.
14) When using Excel to simulate a system, it is necessary to compute only the probability (relative frequency) distribution.
15) Excel can only be used to simulate systems that can be represented by continuous random variables.
16) In Excel the “VLOOKUP” function is used to determine values for continuous random variables.
17) Developing the cumulative probability distribution helps to determine random number ranges.
18) Starting conditions have no impact on the validity of a simulation model.
19) Simulations should always be started with an empty system.
20) Manual simulation is limited because of the amount of real time required to simulate even one trial.
21) __________ is a technique for selecting numbers randomly from a probability distribution.
22) Developing the __________ probability distribution helps to determine random number ranges.
23) Random numbers of a mathematical process instead of a physical process are __________ numbers.
24) Simulation models must be __________ to make sure they are accurately replicating the system being simulated.
25) A table of random numbers must be __________ distributed, efficiently generated, and absent of patterns.
26) The __________ command is used in generating the random numbers with Excel.
27) In order to determine the value of discrete demand in a simulation model using Excel, the __________ function is used to associate a specific value of demand with a random number.
28) The __________, a 10 kilometer race held in Colorado, used simulation to help deal with queuing problems at the finish line.
29) __________ is a risk analysis and forecasting program that uses Monte Carlo simulation.
30) __________, __________, and __________ are common application of simulation.
31) Consider the following distribution and random numbers:
If a simulation begins with the first random number, what would the first simulation value would be __________.
The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.
32) Determine the drying time for these 5 random numbers: 0.13; 0.09; 0.19; 0.81; and 0.12.
33) Determine the drying time for these 5 random numbers: 0.53; 0.95; 0.97; 0.96; and 0.07.
34) The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.
What is the average drying time if you simulate the 10 trials using these random numbers: 0.13; 0.09; 0.19; 0.81; 0.12; 0.53; 0.95; 0.97; 0.96; and 0.07.
35)
Determine the random number ranges for the above data set (Start with 00).
36) Given the following random number ranges and the following random number sequence: 62, 13, 25, 40, 86, 93, determine the average demand for the following distribution of demand.
Demand Random
Number Ranges
5 00-14
6 15-44
7 45-69
8 70-84
9 85-99
37) If f(x) = 2x, what is the equation for generating x, given the random number r?
38) The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.
Compute the mean drying time.
39) A normal distribution has a mean of 500 and a standard deviation of 50. A manager wants to simulate 2 values from this distribution, and has drawn these random numbers: -0.6 and 1.4. What are the 2 values respectively?
40) The number of cars arriving at Joe Kelly’s oil change and tune-up place during the last 200 hours of operation is observed to be the following:
Determine the probability distribution of car arrivals.
41) The number of cars arriving at Joe Kelly’s oil change and tune-up place during the last 200 hours of operation is observed to be the following:
Based on the above frequencies, use two digit random numbers, start with random number 00 and determine the random number ranges for the data set given above.
42) Consider the following manual simulation of machine breakdowns and repair
Breakdowns Time between breakdowns, x (weeks) Repair time, y (days) Cost (\$2,000 y)
1 4 1 \$2000
2 5.7 2 \$4000
3 5.5 2 \$4000
4 2.5 1 \$2000
5 5.2 2 \$4000
6 5.8 2 \$4000
7 1.6 1 \$2000
8 2.3 2 \$4000
9 1.2 2 \$4000
10 3.3 2 \$4000
What operating characteristics can be obtained from this simulation?
43) George Nanchoff owns a gas station. The cars arrive at the gas station according to the following inter-arrival time distribution. The time to service a car is given by the following service time distribution. Using the following random number sequence: 92, 44, 15, 97, 21, 80, 38, 64, 74, 08, estimate the average customer waiting time , average idle time of the assistant and the average time a car spends in the system.
Interarrival time (in minutes) P(X) Random Numbers Service Time (in minutes) P (X) Random Numbers
4 .35 00-34 2 .30 00-29
7 .25 35-59 4 .40 30-69
10 .30 60-89 6 .20 70-89
20 .10 90-99 8 .10 90-99
44) An answering service for a doctor’s office wants to evaluate the service by simulation calls. They used past data to determine the distributions for the time between calls and the time spent on the phone with patients.
Use the table below to manually simulate 8 calls. The time of the call and the service time have already been determined.
Customer
Number Time of
Time Time call ends Customer
Wait Time Operator
Wait Time
1 15 15 25 40 0 15
2 45 45 25 70 0 5
3 70 15
4 95 45
5 125 15 155
6 150 35
7 175 190 25 15 0
8 205 25 240 10 0
Calculate the average waiting time per customer.
Calculate the utilization of the operator.
A graduate research assistant “moonlights” at the short order counter in the student union snack bar in the evenings. He is considering asking for help taking orders, but needs to convince the management that they should hire another student. Because he is taking a simulation class, he thinks it may be the perfect way to convince management to hire more help if he can show that customers have to wait a long time. When a customer arrives, he takes their order and their payment, prepares the food, gives it to the customer, and then takes the order from the next person in line. If someone arrives while he’s cooking an order, they have to wait until he’s completed the current order. He is working on the simulation and a portion is shown below.
45) Complete the table below and determine the average customer wait time.
Customer
Number Time of
Arrival Time Order Taken Order Prep Time Customer Receives Food Customer Wait Time
1 2 2 4 6 0
2 14 14 7
3 19 6
4 28 8
5 33 4
46) Complete the table and determine the average customer waiting time and the utilization of the cook.
Customer Number Time of Arrival Time Order Taken Order Prep Time Customer Receives Food Customer Wait Time Cook “Idle” TIme
1 2 2 4 6 0 2
2 14 14 7
3 19 6
4 28 8
5 33 4
Complete the table and determine the average customer waiting time and the utilization of the cook.
47) Assume that order prep time is based on the following distribution:
Prep Time Probability
3 .10
4 .20
5 .25
6 .20
7 .15
8 .10
Complete the following table given that the random numbers for order prep time for customers 3, 4, and 5 are 62, 93 and 26, respectively.
Arrival
Number Time of
Arrival Time Order Taken Order Prep Time Customer Receives Food Customer Wait Time Cook “Idle” Time
1 1 1 4 5 0 1
2 5 5 7 12 0 0
3 7
4 10
5 18
What is the average customer waiting time and the graduate student’s utilization?
A newsboy sells newspapers and his goal is to maximize profit. He kept a record of his sales for 125 days with the following result:
Newspapers demand per day Number of days
15 10
16 20
17 42
18 31
19 12
20 10
Total 125
His ordering policy is to order an amount each day that is equal to the previous day’s demand.
A newspaper costs the carrier 50 centers and he sells it for \$1.00. Unsold papers are returned and he receives 25 cents (for a loss of 25 cents).
48) Develop the cumulative distribution table and the corresponding random numbers.
Newspapers demanded per day Number of Days Probability Cumulative Probability
15 10
16 20
17 42
18 31
19 12
20 10
Total
49) Use the information and random numbers given in the table below to simulate the sale of newspapers for 10 days.
Day Demand Random Number Quantity Ordered Sales Unsatisfied Demand Unsold Papers
1 .78 18
2 .43
3 .93
4 .87
5 .48
6 .84
7 .87
8 .27
9 .20
10 .52
After completing the simulation, determine his total revenue for the ten days as well as monetary losses that result from unmet demand and unsold papers.
50) Analogue simulation replaces a physical system with an analogous physical system that is __________ to manipulate.
A) harder
B) easier
C) equally difficult
D) none of the above
51) __________ is a technique for selecting numbers randomly from a probability distribution.
A) Marseille
B) Monaco
C) Monte Carlo
D) Analogue simulation
E) all of the above
52) In the Monte Carlo process, values for a random variable are generated by __________ a probability distribution.
A) sampling from
B) running
C) integrating
D) implementing
53) The __________ process is analogous to gambling devices.
A) Simulation
B) Monte Carlo
C) Monaco
D) none of the above
54) __________ numbers are numbers derived from a mathematical process that appear to be random.
A) Random
B) Pseudorandom
C) Randomized
D) Semi-random
55) Pseudorandom numbers exhibit __________ in order to be considered truly random.
A) a limited number of possible outcomes
B) a uniform distribution
C) a detectable pattern
D) a detectable run of certain numbers
56) __________ is not part of a Monte Carlo simulation.
A) Analyzing results
B) Analyzing a real problem
C) Finding an optimal solution
D) Evaluating the results
57) A seed value is a(n)
A) steady state solution of a simulation experiment
B) number used to start a stream of random numbers
C) first run of a simulation model
D) analytic solution of a simulation experiment
58) In assigning random numbers to probabilistic events in a simulation,
A) several events are associated with the same random number
B) every random number is associated with a particular event
C) every event is associated with the same random number
D) all of the above
59) __________ are the values that express the state of the system being modeled at the beginning of the Monte Carlo simulation.
A) Outputs
B) Random events
C) Initial conditions
D) Random numbers
60) Simulation does not usually provide recommended decisions. Instead it provides
A) operating characteristics
B) optimal solutions
C) realistic results
D) system parameters
61) For the following frequency distribution of demand, the random number 0.23 would be interpreted as a demand of:
A) 0
B) 1
C) 2
D) 3
Consider the following frequency of demand and random numbers:
Random numbers: 0.13, 0.81, 0.53.
62) If the simulation begins with the first random number the simulated value for demand would be
A) 0
B) 1
C) 2
D) 3
63) If the simulation begins with the second random number the simulated value for demand would be
A) 1
B) 2
C) 3
D) 4
64) If the simulation begins with the third random number the simulated value for demand would be
A) 0
B) 1
C) 2
D) 3
E) 4
65) Which of the following would not be considered a limitation of simulation modeling?
A) Models are typically unstructured.
B) Validation of simulation models can be difficult.
C) The cost of building simulation can be prohibitive.
D) Simulation allows flexibility in analyzing systems.
Key words: simulation models, limitations
66) Simulations are normally done
A) manually
B) in a casino
D) on the computer
67) Random numbers generated by a __________ process instead of a __________ process are pseudorandom numbers.
A) physical / physical
B) physical / mathematical
C) mathematical / physical
D) mathematical / mathematical
68) A table of random numbers must be
A) uniform
B) efficiently generated
C) absent of patterns
D) all of the above
69) Developing the cumulative probability distribution helps to determine
A) simulation numbers
B) data sets
C) random number ranges
D) all of the above
A graduate research assistant “moonlights” at the short order counter in the student union snack bar in the evenings. He is considering asking for help taking orders, but needs to convince the management that they should hire another student. Because he is taking a simulation class, he thinks it may be the perfect way to convince management to hire more help if he can show that customers have to wait a long time. When a customer arrives, he takes their order and their payment, prepares the food, gives it to the customer, and then takes the order from the next person in line. If someone arrives while he’s cooking an order, they have to wait until he’s completed the current order. He has simulated 5 orders.
Customer Number Time of Arrival Time Order Taken Order Prep Time Customer Receives Food Customer Wait Time
1 2 2 4 6 0
2 14 14 7
3 19 6
4 28 8
5 33 4
70) Average customer waiting time is:
A) 0 minutes
B) 1 minute
C) 2 minutes
D) 2.5 minutes
E) 3 minutes
71) Average utilization is:
A) 50%
B) 67%
C) 72.5%
D) 83.4%
E) 95%
72) __________ simulation is limited because of the amount of real time required to simulate even one trial.
A) Manual
B) Monte Carlo
C) Monaco
D) Any kind of
73) If the probability of an event is 0.36, what random number range specifies this properly?
A) 0.10 – 0.20
B) 0.20 – 0.30
C) 0.30 – 0.40
D) 0.40 – 0.50
74) Sometimes manual simulation of several trials is __________ way to validate a simulation.
A) a good
C) no
D) the only
75) Unlike optimization models, simulation provides
A) recommendations
B) operating characteristics
C) suggestions
D) solutions
76) A limitation of simulation is
A) models are typically unstructured and must be developed for problems that are also unstructured
B) it is often impossible to realistically validate simulation results
C) model building is costly and time-consuming
D) all of the above
The U.S. Department of Agriculture estimates that the yearly yield of limes per acre is distributed as follows:
Yield, bushels per acre Probability
350 .10
400 .18
450 .50
500 .22
The estimated average price per bushel is \$16.80.
77) What is the expected yield of the crop?
A) 425
B) 442
C) 440
D) 475
78) Use the following random numbers to simulation crop yield for 10 years: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81, 31, 89. What is the estimated crop yield from the simulation?
A) 425
B) 442
C) 440
D) 475
79) Use the following random numbers to simulation crop yield for 10 years: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81, 31, 89. What is the estimated crop yield from the simulation?
A) 425
B) 442
C) 440
D) 475
A bakery is considering hiring another clerk to better serve customers. To help with this decision, records were kept to determine how many customers arrived in 10-minute intervals. Based on 100 ten-minute intervals, the following probability distribution and random number assignments developed.
Number of Arrivals Probability Random numbers
6 .1 .01 – .10
7 .3 .11 – .40
8 .3 .41 – .70
9 .2 .71 – .90
10 .1 .91 – .00
80) Suppose the next three random numbers were .18, .89 and .67. How many customers would have arrived during this 30-minute period?
A) 22
B) 23
C) 24
D) 25
E) none of the above
81) Suppose the next three random numbers were .08, .50 and .69. How many customers would have arrived during this 30-minute period?
A) 22
B) 23
C) 24
D) 25
E) none of the above
82) Suppose the next three random numbers were .11, .42 and .84. Use these values to simulate arrivals into the bakery and determine the average number of arrivals per 10-minute period based on these occurrences. The average number of arrivals per 10-minute period is:
A) 6
B) 7
C) 8
D) 9
E) none of the above
Two hundred simulation runs were completed using the probability of a machine breakdown from the table below. The average number of breakdowns from the simulation trials was 1.93 with a standard deviation of 0.20.
No. of breakdowns per week Probability Cumulative probability
0 .10 .10
1 .25 .35
2 .36 .71
3 .22 .93
4 .07 1.00
83) What is the probability of 2 or fewer breakdowns?
A) .10
B) .25
C) .35
D) .36
E) .71
84) What is the probability that there are more than 3 breakdowns?
A) .07
B) .10
C) .22
D) .25
E) .36
85) Construct a 95% confidence interval for the average number of machine breakdowns.
A) 1.896 to 1.938
B) 1.902 to 1.958
C) .1.877 to 1.943
D) 1.907 to 1.953
E) none of the above
86) The use of simulation to determine the impact of projects such as nuclear power plants, reservoirs and dams is known as
A) public service operation
B) environmental and resource analysis
C) cost benefit analysis
D) none of the above
87) The use of simulation to analyze airport operations, and fire or police department operations are known as
A) public service operation
B) environmental and resource analysis
C) cost benefit analysis
D) none of the above
Introduction to Management Science, 10e (Taylor)
Chapter 15 Forecasting

1) A trend is a gradual, long-term, up or down movement of demand.
2) A seasonal pattern is an up-and-down repetitive movement within a trend occurring periodically.
3) Random variations are movements that are not predictable and follow no pattern.
4) The basic types of forecasting methods include time series, regression, and qualitative methods.
5) Time series is a category of statistical techniques that uses historical data to predict future behavior.
6) Regression methods attempt to develop a mathematical relationship between the item being forecast and factors that cause it to behave the way it does.
7) Qualitative methods use management judgment, expertise, and opinion to make forecasts.
8) Qualitative methods are the least common type of forecasting method for the long-term strategic planning process.
9) A cycle is an up and down movement in demand that repeats itself in less than 1 year.
10) Seasonal patterns are observed only during the 4 seasons – winter, spring, summer and fall.
11) The Delphi develops a consensus forecast about what will occur in the future.
12) Technological forecasting helps determine the technological feasibility of new products by surveying large numbers of consumers.
13) Irregular variations exhibit no pattern.
14) Data cannot exhibit both trend and cyclical patterns.
15) Time series methods assume that what has occurred in the past will continue to occur in the future.
16) Moving averages are good for stable demand with no pronounced behavioral patterns.
17) Longer-period moving averages react more slowly to recent demand changes than do shorter-period moving averages.
18) Shorter-period moving averages react more slowly to recent demand changes than do longer-period moving averages.
19) In a weighted moving average, weights must sum to one.
20) Adjusted exponential smoothing is an exponential smoothing forecast adjusted for seasonality.
21) If average forecast error is positive, it indicates that the forecast is biased high.
22) __________ is a gradual long term upward or downward movement of demand.
23) A(n) __________ forecast typically encompass a period longer than one years.
24) __________ error is the sum of the forecast errors.
25) A(n) __________ forecast encompasses the immediate future, is concerned with daily activities of the firm and does not go beyond one or two months in to the future.
26) A(n) __________ is an up-and-down repetitive movement within a trend occurring periodically.
27) __________ relates demand to two or more independent variables.
28) One problem with multiple regression is __________, which is a measure of the amount of “overlapping” information about he dependent variable that’s provided by several independent variables.
29) Exponential smoothing forecasts are more sensitive or reactive to the changes in demand as the value of the smoothing constant, α __________.
30) The closer the value of α is to zero, the __________ will be the dampening or smoothing effect.
31) __________ measures the strength of the relationship between two variables.
32) The __________ is the percentage of variation in the dependent variable that results from the independent variable.
33) Longer period moving averages react more __________ to recent demand changes than do shorter period moving averages.
34) The __________ movements or variations in demand exhibit no pattern and occur on a random basis.
35) The __________ is the sum of the absolute value of forecasting errors divided by the number of periods in which a forecast was made.
36) The __________ is the square of the average of the sum of the squared errors.
37) MAPD measures __________.
38) __________ is a type of exponential smoothing that can also include trend.
Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame:
39) Compute a 3-period moving average for period 4.
40) Compute a 3-period moving average for period 6.
41) Compute a 3-period moving average for period 7.
42) Compute a 5-period moving average for period 6.
43) Compute a 5-period moving average for period 7.
44) Daily highs in Sacramento for the past week (from least to most recent) were: 95, 102, 101, 96, 95, 90 and 92. Develop a forecast for today using a 2 day moving average.
45) Daily highs in Sacramento for the past week (from least to most recent) were: 95, 102, 101, 96, 95, 90 and 92. Develop a forecast for today using a 3 day moving average.
46) Daily highs in Sacramento for the past week (from least to most recent) were: 95, 102, 101, 96, 95, 90 and 92. Develop a forecast for today using a weighted moving average, with a weights of .6, .3 and .1, where the highest weights are applied to the most recent data.
Given the following data on hotel check-ins for a 6-month period:
July: 70 rooms
August: 105 rooms
September: 90 rooms
October: 120 rooms
November: 110 rooms
December: 115 rooms
47) What is the 3-month moving average forecast for January?
48) With alpha = 0.2, what is the simple exponential smoothing forecast for October? Assume the forecast for July was 12 rooms.
49) Using a 3-month moving average, how many check-ins can be forecasted for January?
50) Using the exponential smoothing factor 0.3, how many check-ins can be forecasted for January? Assume the forecast for December was 22 rooms.
51) The following data summarizes the historical demand for a product.
Month Actual Demand
March 20
April 25
May 40
June 35
July 30
August 45
Use exponential smoothing with α = .2 and the smoothed forecast for July is 32 and determine August and September’s smoothed forecasts.
52) If the forecast is 33 and the actual value is 44, then the error this period is
53) If the forecast is 25 and the actual value is 25, then the error this period is
54) The following sales data are available for 2003-2008 :
Determine a 4-year moving average forecast for 2008 and 2009.
55) The following sales data are available for 2003-2008 :
Year Sales Forecast
2003 7 9
2004 12 10
2005 14 15
2006 20 22
2007 16 18
2008 25 21
Calculate the average error.
56) If the forecast is 14 and the actual value is 15, then the error this period is
57) If the absolute errors were calculated for 5 periods and the sum of the absolute deviation is 60, what is the value of the MAD?
58) Assume that the forecasted demand for 2006 is 15, use the following data set and exponential smoothing with α = 0.4 and determine the forecasted demand for 2009.
59) Given the following data, compute the MAD for the forecast.
Year Demand Forecast
2001 16 18
2002 20 19
2003 18 24
60) The following sales data are available for 2003-2008.
Determine a 4-year weighted moving average forecast for 2009, where weights are W1 = .1, W2 = .2, W3 = .2 and W4 = .5.
61) Quarterly sales is given for the past 3 years, determine the seasonal factors for each quarter.
Winter Spring Summer Fall
Year 1 4800 4500 4100 5500
Year 2 570 3800 4500 6000
Year 3 6000 4600 4900 6500
Month Actual Demand
February 20
March 22
April 33
May 35
June 31
July 48
August 41
62) Determine the forecasted demand for April and May based on adjusted exponential smoothing with α = .2, β = .3.
63) The forecasted demand for May, June, July August and September are 25, 30, 33, 38, 40 respectively. Determine the MSE and MAD.
64) Forecasted demand for May, June, July August and September are 25, 30, 33, 38, 40 respectively. Determine the MAPD
65) Base on a three month weighted moving average with weights w1 = .1, w2 = .4, and w3 = .5, determine the forecasted demand for August and September. What is the forecast error in August?
66) Use simple exponential smoothing with alpha = .4 and determine the forecasted demand for August and September. Assume that the smoothed forecast for July is 38.
67) Simple exponential smoothing is being used to forecast demand. The previous forecast of 66 turned out to be four units less than actual demand. If the next forecast is 66.6, what is the value of the smoothing constant, α ?
68) Robert wants to know if there is a relation between money spent on gambling and winnings.
What is the coefficient of determination?
Robert has the following accounts on money spent on gambling and winnings:
69) Develop a regression equation that relates the money Robert spends and the money he wins.
70) Determine the correlation coefficient and the coefficient of determination.
Sally has been running the following number of adds in the local newspaper to help attract customers into her store. She has also been keeping track of customers who have come into the store as a result of the ads, as well as the amount of money they spend.
This is the data from the last 4 weeks:
71) Determine the equation that relates ads and increased sales.
72) If Sally runs 15 ads, how much will sales increase?
73) If Sally runs 10 ads, how much will sales increase?
Consider the following annual sales data for 2001-2008.
Year Sales
2001 2
2002 4
2003 10
2004 8
2005 14
2006 18
2007 17
2008 20
74) Use the linear regression method and determine the estimated sales equation.
75) Calculate the coefficient of determination.
76) Calculate the correlation coefficient .
The following data summarizes the historical demand for a product
Month Actual Demand
March 20
April 25
May 40
June 35
July 30
August 45
77) Use a four period moving average to determine the forecasted demand for July, August and September.
78) If the forecasted demand for June, July and August is 32, 38 and 42, respectively, what is MAD?
79) If the forecasted demand for June, July and August is 32, 38 and 42, respectively, what is MSE?
80) If the forecasted demand for June, July and August is 32, 38 and 42, respectively, what is MAPD?
81) A manager uses the following equation to predict monthly receipts: Yt = 4,000 + 30t. What is the forecast for July of next year if t = 0 in April of this year?
82) A local gym has discovered that their demand for personal trainers (measured in hours) is related not only to their own advertising expenditures in the prior month, but also to the demand for doughnuts and swim gear in the prior month at neighboring stores. The gym has developed the following regression model to forecast demand for personal trainers:
Demand = 185 + (0.15*advertising expenditures) – (0.05*doughnuts) + (0.23*swim gear sales)
What is the forecast for October, given advertising expenditures of 1000, doughnut sales of 2450, and swim gear sales of 782 in September?
83) Managers use __________ in forecasting.
A) judgment
B) opinion
C) past experience
D) all of the above
84) The applicability of forecasting methods depends on
A) the time frame of the forecast
B) the existence of patterns in the forecast
C) the number of variables to which the forecast is related
D) all of the above
85) __________ is a gradual, long-term, up or down movement of demand.
A) Seasonal pattern
B) Cycle
C) Trend
D) Prediction
86) A __________ is an up-and-down repetitive movement that repeats itself over a time span of more than 1 year.
A) prediction
B) seasonal pattern
C) trend
D) cyclical pattern
87) __________ methods are the most common type of forecasting method for the long-term strategic planning process.
A) Regression
B) Qualitative
C) Time series
D) all of the above
88) __________ is a category of statistical techniques that uses historical data to predict future behavior.
A) Qualitative methods
B) Regression
C) Time series
D) Quantitative methods
89) __________ use management judgment, expertise, and opinion to make forecasts.
A) Qualitative methods
B) Regression
C) Time series
D) Quantitative methods
90) The __________ is a procedure for developing a consensus forecast about what will occur in the future.
A) Delphi method
B) quantitative method
C) regression equation
D) time series forecasting method
91) __________ has become increasingly crucial to compete in the modern international business environment.
A) The Delphi method
B) Technological forecasting
C) Prediction
D) all of the above
92) Consider the following graph of sales.
Which of the following characteristics is exhibited by the data?
A) Trend only
B) Trend plus seasonal
C) Trend plus random
D) Cyclical only
E) None of the above
93) Consider the following graph of sales.
Which of the following characteristics is exhibited by the data?
A) Trend only
B) Trend plus seasonal
C) Trend plus random
D) Seasonal only
E) None of the above
94) Consider the following graph of sales.
Which of the following characteristics is exhibited by the data?
A) Trend only
B) Trend plus seasonal
C) Trend plus irregular
D) Seasonal
E) None of the above
95) __________ moving averages react more slowly to recent demand changes than do __________ moving averages.
A) Longer-period, shorter-period
B) Shorter-period, longer-period
C) Longer-period, longer-period
D) Shorter-period, shorter-period
96) __________ is good for stable demand with no pronounced behavioral patterns.
A) Longer-period moving average
B) Shorter-period moving average
C) Moving average
D) Weighted moving average
97) __________ methods assume that what has occurred in the past will continue to occur in the future.
A) Time series
B) Regression
C) Quantitative
D) Qualitative
98) In exponential smoothing, the closer alpha is to __________, the greater the reaction to the most recent demand.
A) -1
B) 0
C) 1
D) -1 or 1
99) In adjusted exponential smoothing, the closer beta is to __________, the stronger a trend is reflected.
A) -1 / 1
B) -1
C) 0
D) 1
100) __________ is a linear regression model relating demand to time.
A) Linear trend
B) Linear regression
C) Forecast demand
D) Linear equation
101) Which of the following possible values of alpha would cause exponential smoothing to respond the most slowly to sudden changes in forecast errors?
A) .01
B) .10
C) .20
D) .50
E) .90
102) Given an actual demand of 59, a previous forecast of 64, and an alpha of .3, what would the forecast for the next period be using simple exponential smoothing?
A) 36.9
B) 57.5
C) 60.5
D) 62.5
E) 65.5
103) __________ is the difference between the forecast and actual demand.
A) Forecast mistake
B) Forecast error
D) Forecast accuracy
104) __________ is absolute error as a percentage of demand.
A) Cumulative error
C) MAPD
D) Average error
105) __________ indicates a forecast is biased low.
A) Large :
B) Large –
C) Large +
D) Large x
106) __________ indicates a forecast is biased high.
A) Large +
B) Large –
C) Large :
D) Large x
107) __________ is a measure of the strength of the relationship between independent and dependent variables.
A) Correlation
B) Linear regression
C) Coefficient of determination
D) Regression
108) __________ is the percentage of the variation in the dependent variable that results from the independent variable.
A) Regression
B) Coefficient of determination
C) Correlation
D) Linear regression
109) Coefficient of determination is the percentage of the variation in the __________ variable that results from the __________ variable.
A) dependent, dependent
B) independent, dependent
C) dependent, independent
D) independent, independent
110) Consider the following demand and forecast.
Period Demand Forecast
1 7 10
2 12 15
3 18 20
4 22
If MAD = 2, what is the forecast for period 4?
A) 19
B) 20
C) 21
D) 22
E) none of the above
Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame:
111) Use a 2-period moving average to forecast demand for period 7.
A) 227.5
B) 275
C) 280
D) 290
E) none of the above
112) Use a 3-period moving average to forecast demand for period 7.
A) 283.33
B) 280
C) 290
D) 310
E) none of the above
113) If the forecast for period 5 is equal to 275, use exponential smoothing to compute a forecast for period 7 if α = .40.
A) 273
B) 277
C) 267.8
D) 286.2
E) none of the above
The following data represents quarterly sales of lawnmowers.

Year Quarter 1 Quarter 2 Quarter 3 Quarter 4
1 150 140 190 165
2 160 148 210 175
114) What is the seasonal index for the third quarter? (Round to the nearest hundredth.)
A) .20
B) .22
C) .26
D) .30
E) none of the above
115) What is the seasonal index for the fourth quarter? (Round to the nearest hundredth.)
A) .20
B) .23
C) .25
D) .30
E) none of the above
116) The manager of “Skis 4 U” is preparing a forecast for February of 2011. Demand exhibits both trend and seasonality. The trend equation for monthly demand is y = 4375 + 80t, where t = 1 for January 2009. The seasonal index for February is 1.25. The forecast for February is
A) 4575
B) 4583
C) 5719
D) 5729
E) none of the above
117) Given forecast errors of 6, 4, 0 and -2, what is the mean absolute deviation?
A) 2
B) 3
C) 4
D) 2.67
E) none of the above
118) Given forecast errors of 6, 4, 0 and -2, what is the mean squared error?
A) 14
B) 18.67
C) 16
D) 12
E) none of the above
Introduction to Management Science, 10e (Taylor)
Chapter 16 Inventory Management

1) Independent demand items are used internally to produce a final product.
2) Dependent demand items are final products demanded by an external customer.
3) Inventory costs include carrying, ordering, and shortage costs.
4) The purpose of inventory management is to determine how much and when to order.
5) In a continuous inventory system, a constant amount is ordered when inventory declines to a predetermined level.
6) In a periodic inventory system, a constant amount is ordered when inventory declines to a predetermined level.
7) The EOQ is the optimal order quantity that will minimize total carrying costs.
8) Assumptions of the basic EOQ model include constant demand, no shortages, constant lead time, and gradual usage.
9) The non-instantaneous receipt model applies only to manufacturing.
10) The EOQ model with shortages does not allow backorders.
11) The basic EOQ model plays no role in determining order sizes in the presence of quantity discounts.
12) Quantity discounts are always evaluated with carrying cost as a percentage of price.
13) The service level is the probability that the inventory available during lead time will meet demand.
14) If service level is 50%, then safety stock is equal to 50% of lead time demand.
15) The reorder point is the date when a new order should be placed.
16) If lead time and demand are constant, safety stock is equal to demand multiplied by lead time.
17) Periodic inventory systems normally require smaller safety stock than a continuous inventory system.
18) Techniques for inventory analysis are widely used to analyze other types of problems.
19) Carrying costs include storage cost, interest and depreciation.
20) Ordering costs include transportation, shipping and inspection.
21) Shortage costs include loss of customer goodwill.
22) If a business frequently runs out of inventory their service levels are negative.
23) __________ demand items are generally final products demanded by customers.
24) The purpose of inventory management is to determine __________ and __________ to order.
25) __________ demand items are used internally to produce a final product.
26) Inventory __________ costs include storage cost and the cost of capital.
27) Inventory __________ costs include transportation and inspection.
28) A __________ occurs when customer demand cannot be met because of insufficient inventory.
29) In a __________ inventory system, a constant amount is ordered when inventory declines to a predetermined level.
30) In a __________ inventory system an order is placed for a variable amount after a fixed passage of time
31) __________ is the optimal order quantity that will minimize the total inventory costs.
32) A __________ occurs when an item is out of stock and is sold to the customer when a shipment arrives.
33) Costs involved in a typical inventory model include __________ and __________.
34) In the basic EOQ model, as the size of the order increases, the annual __________ cost decreases.
35) In the basic EOQ model, as the size of the order increases, the annual __________ cost increases.
36) In the quantity discounts model, the __________ must be included in the total cost calculation. This variable is not included in the basic EOQ model.
37) If all the variables are held constant, the total inventory cost in a non-instantaneous receipts model is __________ than the total cost in the basic EOQ model.
38) The __________ determines when an order should be placed for a continuous review inventory system.
39) __________ is inventory that is used to help protect against stockouts.
40) __________ is the probability that the inventory available during the lead time will meet demand.
41) If lead time and demand are constant then __________ is zero.
42) For the __________ inventory system, Q, the quantity ordered, can vary.
43) The EOQ model is __________ , or resistant to errors in the cost estimates and demand.
44) __________ costs and _________ costs react inversely to each other in response to an increase in order size.
45) The basic EOQ model assumes that __________ is known with certainty and is relatively constant over time.
46) In the basic EOQ model, if D=80 per month, Co=\$13, and Cc=\$11 per unit per month, what is the EOQ?
47) In the basic EOQ model, if D=40 per month, Co=\$9, and Cc=\$8 per unit per month, what is the EOQ?
48) In the basic EOQ model, if D=100 per month, Co=\$20, and Cc=\$15 per unit per month, what is the EOQ?
49) In the basic EOQ model, if annual demand is 50 units, carrying cost is \$2 per unit per year, and ordering cost is \$15, what is the EOQ?
A company produces item Y, and uses the basic EOQ model for managing its inventory. Lead time to obtain item Y is two weeks. Demand is normally distributed with a mean of 400 units per week and a standard deviation of 40 units per week. The desired service level is 98.5%. The ordering cost is \$20, and carrying cost is 20% of the items cost, which is \$10.
50) Determine the order quantity for product Y. (Assume 52 weeks of operation per year.)
51) Determine the annual setup cost and the annual carrying cost for product Y. (Assume 52 weeks of operation per year.)
52) Determine the total annual inventory cost for product Y. Include the item cost in your calculations. (Assume 52 weeks of operation per year.)
53) Determine the reorder point for product Y.
The injection molding department of Alver Inc. uses an average of 40 pounds of a special powder per day. The plant operates 250 days per year. The daily usage of the powder is normally distributed with a standard deviation of 5 pounds per day. The lead time to obtain the powder from a supplier is 9 days. The annual holding cost is \$2. per unit and the cost of ordering the powder is \$50.
54) How many units should Alver Inc. order in order to minimize annual ordering and carrying cost?
55) How many orders will be placed each year?
56) Determine the reorder point for a service level of 97%.
The daily sales of a peanut butter at Power’s Grocery are normally distributed, with a mean of 12 jars and a standard deviation of 4. The manager checks the inventories on shelves and places an order every three days. Delivery lead time is two days.
57) How much safety stock of peanut butter should they have for a 99% service level?
58) If there are 4 jars on the shelf when an order is placed, how much should the store order?
59) The daily demand for a product is normally distributed with a mean of 80 and a standard deviation of 8. Constant lead time is 4 days. The cost of placing an order is \$20. The item costs \$8 and the carrying rate per year is 10% of the item cost. Determine the economic order quantity.
60) In a non-instantaneous receipt model, daily demand is 55 units and daily production is 120 units, Co=\$70 and Cc=\$4 per unit/year. The production facility operates 300 days per year. What is the maximum inventory level?
61) In a non-instantaneous receipt model, daily demand is 55 units and daily production is 120 units, Co=\$70 and Cc=\$4 per unit/year. The production facility operates 300 days per year. What is the optimal order quantity?
62) A product has an annual demand of 3600 units. Unit cost for this product is \$3. Set up cost is \$20 and the inventory carrying rate as a percent of the unit cost is 25%. The product is produced in-house where the daily production rate is 50 units. Assume 360 working days per year and determine the economic production quantity.
63) A product has an annual demand of 3600 units. Unit cost for this product is \$3. Set up cost is \$20 and the inventory carrying rate as a percent of the unit cost is 25%. The product is produced in-house where the daily production rate is 50 units. Assume 360 working days per year and determine the annual ordering cost and carrying cost.
64) Given an EOQ model with shortages in which annual demand is 4200 units, Co=\$160, Cc=\$7 per unit per year and CS =\$25, what is the total annual shortage cost?
65) Given an EOQ model with shortages in which annual demand is 4200 units, Co=\$160, Cc=\$7 per unit per year and CS =\$25, what is the optimal order quantity?
66) Given an EOQ model with shortages in which annual demand is 4200 units, Co=\$160, Cc=\$7 per unit per year and CS =\$25, what is the annual ordering cost?
67) Given an EOQ model with shortages in which annual demand is 4200 units, Co=\$160, Cc=\$7 per unit per year and CS =\$25, what is the optimal stock out level?
68) Given an EOQ model with shortages in which annual demand is 4200 units, Co=\$160, Cc=\$7 per unit per year and CS =\$25, what is the annual carrying cost?
69) Given an EOQ model with shortages in which annual demand is 4200 units, Co=\$160, Cc=\$7 per unit per year and CS =\$25, what is the total minimum annual inventory cost?
A company distributes repair parts for high end appliances. The annual demand is 81,000 and the company operates 300 days per year. The annual carrying cost is 20% of the item cost, which is \$500. The ordering cost is estimated at \$60 and the shortage cost is \$150.
70) Determine the optimal order quantity.
71) Determine the optimal shortage level.
72) How many order per year will they place?
73) What is the maximum inventory level?
74) Determine the annual shortage cost.
75) If the daily demand is 30 and the lead time in days is 3, what is the reorder point?
76) If the daily demand is 67 and the lead time in days is 2, what is the reorder point?
77) If the daily demand is 25 and the lead time in days is 4, what is the reorder point?
78) Sonny Lawler’s law office uses EOQ models to manage their office supplies. They’ve been ordering ink refills for their printers in quantities of 60 units. The firm estimates carrying cost at 40% of the \$10 unit cost and that annual demand is about 240 units per year. The assumptions of the basic EOQ model are thought to apply. For what value of ordering cost would its action be optimal?
79) Dana Swor’s Dream Store sells weight loss products. Her best-selling item, an energy booster and fat burning pill, has an annual demand of 400 units. Ordering cost is \$40 and carrying cost is \$5 per unit year. How many units should she order to minimize total inventory costs?
80) Annual demand for a paperback dictionary at the bookstore is 1200 units. Ordering costs are 350, carrying costs are \$6 per unit per year, and the lead time is 9 days. The bookstore is open for 300 days of the year. What is the reorder point ?
81) If average demand for an inventory item is 200 units per day, lead time is 3 days, and safety stock is 100 units, what is the reorder point?
82) If average demand for an inventory item is 180 units per day, lead time is 5 days, and safety stock is 90 units, what is the reorder point?
83) Annual demand for notecards at Suzie’s Stationery shop is 10,000 units. Deliveries take about 5 working days and Suzie operates 300 days per year. Calculate the reorder point for the notecards that she stocks.
A bakery uses an average of 60 ounces of organic orange juice daily. Demand is normally distributed with a standard deviation of 15 ounces. The bakery places orders every seven days. The lead time for delivery of the juice is three days.
84) Compute the safety stock required to achieve a 98% service level
85) If the bakery has 190 ounces at the time an order is placed, how much should be ordered?
86) The daily demand for a product is normally distributed with a mean of 80 and a standard deviation of 8. Constant lead time is 4 days. The cost of placing an order is \$20. The item costs \$8 and the carrying rate per year is 10% of the item cost. Determine the reorder point to satisfy 90% of the orders.
87) A bakery’s use of corn syrup is normally distributed with a mean of 50 gallons per day and a standard deviation of 5 gallons per day. Lead time for delivery of the syrup is normal with a mean of 4 days and a standard deviation of 2 days. The manager wants a service level of 99 percent. Calculate the reorder point.
88) A bakery’s use of corn syrup is normally distributed with a mean of 50 gallons per day and a standard deviation of 5 gallons per day. Lead time for delivery of the syrup is normal with a mean of 4 days and a standard deviation of 2 days. The manager reorders when his inventory drops to 300 gallons. What cycle service level is implied by this policy?
89) A manager has just received a revised price schedule from a vendor. What order quantity should the manager use in order to minimize total costs? Annual Demand is 120 units, ordering cost is \$10, and annual carrying cost is \$1 per unit.
Quantity Unit Price
1-59 \$15
60-99 \$14
100 or more \$13
90) An office manager uses 400 boxes of file folders per year. The price is \$8.50 per box for an order size of 199 boxes or less, \$8.00 per box for orders of 200 to 799 boxes, and \$7.50 per box for an order of 800 or more boxes. Carrying cost is 20 percent of the price of the product and ordering costs are \$80. What order quantity minimizes total annual cost?
91) __________ demand items are used internally to produce a final product.
A) Independent
B) Dependent
C) Assumed
D) Internal
E) Integrated
92) __________ demand items are final products demanded by an external customer.
A) Assumed
B) Dependent
C) Independent
D) External
E) Integrated
93) Inventory costs include
A) carrying
B) ordering
C) shortage costs
D) all of the above
94) The purpose of inventory management is to determine
A) timing and cost of orders
B) quantity and cost of orders
C) timing and quantity of orders
D) ordering and carrying costs
95) A keyboard costs \$1,000, and the annual holding cost is 25%. Annual demand is 10,000 units, and the order cost is \$150 per order. What is the approximate economic order quantity?
A) 16
B) 70
C) 110
D) 183
96) In a(n) __________ inventory system a constant amount is ordered when inventory declines to a predetermined level.
A) optimal
B) economic
C) periodic
D) continuous
97) In a(n) __________ inventory system, an order is placed for a variable amount after a fixed passage of time.
A) periodic
B) continuous
C) optimal
D) economic
98) EOQ is a(n) __________ inventory system.
A) periodic
B) continuous
C) optimal
D) economic
99) EOQ is the optimal order quantity that will __________ total inventory costs.
A) maximize
B) minimize
D) maintain
E) improve
100) Assumptions of the EOQ model include
A) constant demand and no shortages
C) instantaneous order receipt
D) all of the above
101) In the basic EOQ model, if lead time increases from 5 to 10 days , the EOQ will
A) double
B) increase, but not by double the amount
C) remain the same
D) decrease
102) The economic production quantity is 500 units (units are delivered to the user department as they come off the production line). If the firm decides to buy this item from an outside supplier rather than producing it, the economic purchase quantity would probably be (assume that inventory costs of production and purchasing an item are the same):
A) less than 500 units
B) more than 500 units
C) 500 units
D) the direction of change in quantity cannot be determined without additional information
103) If order quantity is increased, annual holding cost __________, annual order cost __________, and change in annual total cost __________.
A) decreases, increases, is positive
B) decreases, increases, can not be determined
C) decreases, decreases, can not be determined
D) increases, decreases, is negative
E) increases, decreases, can not be determined
104) The EOQ minimizes total __________ cost.
A) inventory
B) purchase
C) ordering
D) marketing
E) carrying
105) In an EOQ model, as the carrying cost increases, the order quantity :
A) increases.
B) decreases.
C) remains the same
D) cannot be determined
106) In the basic EOQ model, if D=60 per month, S=\$12, and H=\$10 per unit per month, what is the EOQ?
A) 11
B) 12
C) 13
D) 14
107) In the basic EOQ model, if annual demand is 50, carrying cost is \$2 per unity per year, and ordering cost is \$15, what is the EOQ?
A) 27.39
B) 26.39
C) 25.39
D) 24.39
E) 22.39
108) The daily sales of a peanut butter at Power’s Grocery are normally distributed, with a mean of 12 jars and a standard deviation of 4. The manager checks the inventories on shelves and places an order every three days. Delivery lead time is two days and they carry 21 jars for safety stock. If there are 4 jars on the shelf when an order is placed, how much should the store order?
A) 77
B) 81
C) 32
D) 36
E) cannot be determined from the information provided
109) In a non instantaneous receipt model, daily demand is 55 units and daily production is 120 units, Co=\$70 and Cc=\$4 per unit per year. What is the maximum inventory level? (Assume that the facility is open 365 days per year)
A) 616.9
B) 618.4
C) 620.3
D) 622.9
E) 625.5
110) A firm is presently purchasing an itme for inventory using the basic EOQ model. They plan on making the product themselves and will be using the EOQ model based on non-instantaneous receipt of inventory. If everything else stays the same, what changes should the firm expect?
A) EOQ decreases
B) Total relevant inventory (annual setup and annual carrying) cost increase
C) Average inventory level decreases
D) Reorder point increases
E) Safety stock increases
111) When using the EOQ Formula with non-instantaneous production, as the demand rate (D) increases more than the rate of production, the EOQ:
A) increases
B) decreases
C) remains the same
D) cannot be determined

112) The diagram above represents which type of inventory model?
A) Economic Order Quantity (EOQ)
B) EOQ with Noninstantaneous Receipt
C) Economic Production Quantity
D) Fixed Period Model
E) none of the above
113) The slope of the line labeled “B” in the diagram above is:
A) Order rate
B) Rate of inventory demand
C) Production rate
D) Shipping rate
E) Production rate minus rate of inventory demand
114) The slope of the line labeled “A” in the diagram below is:
A) Order rate
B) Rate of inventory demand
C) Production rate
D) Shipping rate
E) Production rate minus rate of inventory demand
115) The slope of the line labeled “C” in the diagram below is:
A) Order rate
B) Rate of inventory demand
C) Production rate
D) Shipping rate
E) Production rate minus rate of inventory demand
116) The interval labeled “E” in the diagram below is:
A) Production cycle
B) Production run length
D) Inventory fill rate
117) The interval labeled “D” in the diagram below is:
A) Production cycle
B) Production run length
D) Inventory fill rate
118) A product has demand during lead time of 100 units, with a standard deviation of 25 units. What safety stock (approximately) provides a 95% service level?
A) 41
B) 55
C) 95
D) 140
119) Given an EOQ model with shortages in which annual demand is 4200 units, Co=\$160, Cc=\$7 per unit per year and Cs =\$25, what is the total annual shortage cost?
A) 294.72
B) 296.51
C) 298.53
D) 299.17
E) 285.91
120) Given an EOQ model with shortages in which annual demand is 4200 units, Co=\$160, Cc=\$7 per unit per year and Cs =\$25, what is the order quantity?
A) 394.72
B) 285.91
C) 495.74
D) 296.51
E) 456.34
121) Given an EOQ model with shortages in which annual demand is 4200 units, Co=\$160, Cc=\$7 per unit per year and Cs =\$25, what is the optimal stock out level?
A) 96.44
B) 102.36
C) 108.44
D) 114.64
E) 121.43
122) Given an EOQ model with shortages in which annual demand is 4200 units, Co=\$160, Cc=\$7 per unit per year and Cs =\$25, what is the annual carrying cost?
A) 2711.09
B) 1059.03
C) 1355.55
D) 296.51
E) 495.74
123) Given an EOQ model with shortages in which annual demand is 4200 units, Co=\$160, Cc=\$7 per unit per year and Cs =\$25, what is the annual ordering cost?
A) 2711.09
B) 1059.03
C) 1355.55
D) 296.51
E) 495.74
The manager of the Quick Stop Corner Convenience Store (which is open 360 days per year) sells four cases of Stein soda each day (1,440 cases per year). Order costs are \$8.00 per order. The lead time for an order is three days. Annual holding costs are equal to \$57.60 per case.
124) If the manager orders 16 cases each time she placed an order, what is the average inventory level?
A) 4 cases
B) 8 cases
C) 12 cases
D) 20 cases
E) 16 cases
125) If the manager orders 16 cases each time she placed an order, how many orders would she place in a year?
A) 10
B) 22.5
C) 50
D) 72
E) 90
126) What is the optimal order quantity for Stein soda?
A) 4 cases
B) 8 cases
C) 12 cases
D) 20 cases
E) 16 cases
127) What is the reorder point for Stein soda?
A) 4 cases
B) 8 cases
C) 12 cases
D) 20 cases
E) 16 cases
128) If the daily demand is 50 and the lead time in days is 4, what is the reorder point?
A) 200
B) 220
C) 240
D) 260
E) 300
129) If the daily demand is 40 and the level time in days is 4, what is the reorder point?
A) 120
B) 140
C) 160
D) 180
E) 200
130) If the daily demand is 10 and the level time in days is 8, what is the reorder point?
A) 50
B) 60
C) 70
D) 80
E) 90
131) If average demand for an inventory item is 200 units per day, lead time is 3 days, and safety stock is 100 units, what is the reorder point?
A) 300
B) 500
C) 600
D) 700
E) 800
132) Ruby owns a small café and uses a linen supplier for her tablecloths. Whenever she needs more tablecloths, she calls the supplier. She uses an average of 12 tablecloths a day with a standard deviation of 3 tablecloths. Lead time is a constant 2 days. If Ruby is willing to accept a 5% stockout risk, what is the reorder point, rounded to the nearest tablecloth? Assume demand is normally distributed.
A) 28
B) 31
C) 34
D) 42
E) none of the above
133) The service level is the probability that
A) the inventory will meet demand
B) the inventory available during lead time will meet demand
C) the inventory available during lead time will not meet demand
D) the inventory will not meet demand
134) What service level results in zero safety stock in reorder point calculations?
A) 0%
B) 33%
C) 50%
D) 100%
E) 80%
135) The __________ is the probability that the inventory available during lead time will meet demand.
A) service level
B) inventory level
C) review period
D) reorder point
E) maximum inventory level
136) If annual demand equals 1000 units, the number of working days per year is 250, Co=\$300 per order and Cc=\$3 per unit, how many days are between orders in the basic EOQ model?
A) 105
B) 110
C) 112
D) 115
E) 120
137) Annual demand for a paperback dictionary at a bookstore is 1200 units. The order cost is \$350 and the carrying cost is \$6 per unit per year. The number of working days per year is 365. What is the reorder point? Assume that the basic EOQ model is applicable.
A) 29.2
B) 29.4
C) 29.6
D) 29.8
E) 30.1
138) As service level increases, expected number of stock outs __________ and safety stock __________.
A) increase, increases
B) decrease, decreases
C) decrease, increases
D) increase, decreases
139) Adding 1.5 standard deviations of safety stock to the average demand during lead time will result in a service level of approximately:
A) 50%
B) 68.4%
C) 84.1%
D) 93.3%
E) 97.7%
140) A periodic inventory system
A) uses fixed order sizes at variable time intervals
B) normally requires a larger safety stock
C) cannot be used if demand is variable
D) is used to periodically manage inventory
141) Demand for a product is constant but lead time is variable. The demand during the lead time is normally distributed with a mean of 40 and a standard deviation of 4. They computed a reorder point of 45 units Approximately what service level is being used?
A) 85%
B) 90%
C) 95%
D) 98%
E) none of the above
142) The economic order quantity is especially sensitive to which of the following?
A) ordering cost
B) carrying cost
C) annual demand
E) none of the above
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Mat 540 Quiz 1 Week 2 Chapter 1 and 11 Solution

Introduction to Management Science, 11e (Taylor)
Chapter 1 Management Science

1) Management science involves the philosophy of approaching a problem in a subjective manner.
Diff: 1 Page Ref: 2
Section Heading: The Management Science Approach to Problem Solving
Keywords: scientific approach
AACSB: Analytic skills

2) Management science techniques can be applied only to business and military organizations.
Diff: 1 Page Ref: 2
Section Heading: The Management Science Approach to Problem Solving
Keywords: scientific approach, problem solving
AACSB: Analytic skills

3) Management scientists use the terms “data” and “information” interchangeably–that is, the two terms mean the same thing
Diff: 2 Page Ref: 4
Section Heading: The Management Science Approach to Problem Solving
Keywords: data
AACSB: Analytic skills

4) A management science solution can be either a recommended decision or information that helps a manager make a decision
Diff: 2 Page Ref: 5
Section Heading: The Management Science Approach to Problem Solving
Keywords: model, management science techniques
AACSB: Analytic skills

5) A variable is a value that is usually a coefficient of a parameter in an equation.
Diff: 1 Page Ref: 3
Section Heading: The Management Science Approach to Problem Solving
Keywords: variable
AACSB: Analytic skills
6) Parameters are known, constant values that are usually coefficients of variables in equations.
Diff: 1 Page Ref: 3
Section Heading: The Management Science Approach to Problem Solving
Keywords: parameter
AACSB: Analytic skills

7) Data are pieces of information from the problem environment.
Diff: 1 Page Ref: 4
Section Heading: The Management Science Approach to Problem Solving
Keywords: data
AACSB: Analytic skills

8) A model is a mathematical representation of a problem situation including variables, parameters, and equations.
Diff: 1 Page Ref: 3
Section Heading: The Management Science Approach to Problem Solving
Keywords: model, management science techniques
AACSB: Analytic skills

9) A management science technique usually applies to a specific model type.
Diff: 1 Page Ref: 3
Section Heading: The Management Science Approach to Problem Solving
Keywords: models, management science techniques
AACSB: Analytic skills

10) The first step of the management science process is to define the problem.
Diff: 2 Page Ref: 2
Section Heading: The Management Science Approach to Problem Solving
Keywords: management science process
AACSB: Analytic skills

11) Management science modeling techniques provide results that are known with certainty.
Diff: 2 Page Ref: 17
Section Heading: Management Science Modeling Techniques
Keywords: management science modeling techniques, certainty
AACSB: Analytic skills
12) The term “sensitivity analysis” refers to testing how a problem solution reacts to changes in one or more of the model parameters.
Diff: 1 Page Ref: 10
Section Heading: Model Building: Break-Even Analysis
Keywords: sensitivity analysis, parameter changes

13) Fixed costs depend on the number of items produced.
Diff: 1 Page Ref: 7
Section Heading: Model Building: Break-Even Analysis
Keywords: fixed cost, break-even analysis
AACSB: Analytic skills

14) Variable costs depend on the number of items produced.
Diff: 1 Page Ref: 7
Section Heading: Model Building: Break-Even Analysis
Keywords: variable cost, break-even analysis

15) Fixed cost is the difference between total cost and total variable cost.
Diff: 1 Page Ref: 8
Section Heading: Model Building: Break-Even Analysis
Keywords: total cost, break-even analysis

16) The break-even point is the volume that equates total revenue with total cost.
Diff: 1 Page Ref: 9
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills

17) In general, an increase in price increases the break-even point if all costs are held constant.
Diff: 1 Page Ref: 10
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills
18) If variable costs increase, but price and fixed costs are held constant, the break-even point will decrease.
Diff: 2 Page Ref: 11
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills

19) Managers utilize spreadsheets to conduct their own analyses in management science studies.
Diff: 2 Page Ref: 12
AACSB: Analytic skills

20) Management science techniques focus primarily on observation, model construction, and implementation to find an appropriate solution to a problem.
Diff: 2 Page Ref: 15
Section Heading: Management Science Modeling Techniques
Keywords: mgt science modeling techniques, steps of the scientific method
AACSB: Analytic skills

21) Management science modeling techniques focus on model construction and problem solution.
Diff: 2 Page Ref: 15
Section Heading: Management Science Modeling Techniques
Keywords: mgt science model techniques, model constr, prob solution
AACSB: Analytic skills

22) A typical objective function might be written as 3S + 2R + 5Z ≤ 20.
Diff: 2 Page Ref: 4
Section Heading: The Management Science Approach to Problem Solving
Keywords: objective function
AACSB: Analytic skills

23) Decision Support Systems (DSS) use computers to help decision makers address complex problems.
Diff: 1 Page Ref: 20
Section Heading: Management Science Models in Decision Support Systems
Keywords: decision making, management science
24) In both an objective function and a constraint, the decision variables are represented by numbers.
Diff: 1 Page Ref: 4
Section Heading: The Management Science Approach to Problem Solving
Keywords: decision variables
AACSB: Analytic skills

25) Constraints usually appear as equations that are less than, equal to, or greater than a parameter.
Diff: 1 Page Ref: 4
Section Heading: The Management Science Approach to Problem Solving
Keywords: constraints
AACSB: Analytic skills

26) Enterprise Resource Planning (ERP) system is a data-oriented decision support system that utilizes specific management science solution procedures to solve individual problems such as cost-volume analysis.
Diff: 1 Page Ref: 21
Section Heading: Management Science Models in Decision Support Systems
Keywords: decision support systems

27) A key element of a decision support system (DSS) is the person using the system.
Diff: 2 Page Ref: 20
Section Heading: Management Science Models in Decision Support Systems
Keywords: decision support systems
AACSB: Analytic skills

28) Electronic data interchange (EDI) is a type of decision support system.
Diff: 1 Page Ref: 21
Section Heading: Management Science Models in Decision Support Systems
Keywords: decision support systems
AACSB: Analytic skills

29) A ________ is a symbol used to represent an item that can take on any value.

30) ________ are known, constant values that are coefficients of variables in equations.

31) ________ are pieces of information from the problem environment.

32) A ________ is a functional relationship including variables, parameters, and equations.

33) Management science techniques include ________ techniques, models that are represented as diagrams, presenting a pictorial representation of the system being analyzed.

34) An increase in output typically results in an increase in the ________ cost.

35) ________ techniques provide results that contain uncertainty, unlike mathematical programming techniques which are deterministic.

36) ________ costs are independent of the volume of goods produced and remain constant.

37) The difference between volume multiplied by price and the sum of fixed and variable costs is ________.

38) ________ depend on the number of items produced.

39) Total revenue minus total cost equals ________.

40) The ________ is the volume that equates total revenue with total cost.

41) A ________ represents a limitation to achieving maximum profits due to limited resources.

42) A ________ programming technique refers to a predetermined set of mathematical steps used to solve a problem.

43) One way to test how a management science model reacts to changes in its parameters is to conduct ________ analysis.

44) ________ consist of models that are represented as diagrams rather than as strictly mathematical techniques.

45) A management science technique that does not assume that all parameters are known with certainty is a(n) ________ technique.

46) A ________ is a computer-based system that helps decision-makers address complex problems that involve different parts of an organization and operations.

47) The relationship d = 5000 – 25p describes what happens to demand (d) as price (p) varies. Price can vary between \$10 and \$50. How many units can be sold when the price is \$10?

48) Researchers at John H. Stroger, Jr. Hospital of Cook County used ________ to address the problem of healthcare-associated infections in hospitals.

49) A production process requires a fixed cost of \$50,000. The variable cost per unit is \$25 and the revenue per unit is projected to be \$45. Write a mathematical expression for total cost.

50) A production process requires a fixed cost of \$50,000. The variable cost per unit is \$25 and the revenue per unit is projected to be \$45. Write a mathematical expression for total revenue.

51) A production process requires a fixed cost of \$50,000. The variable cost per unit is \$25 and the revenue per unit is projected to be \$45. Write a mathematical expression for total profit.

52) A production process requires a fixed cost of \$50,000. The variable cost per unit is \$25 and the revenue per unit is projected to be \$45. Find the break-even point.

53) A production process requires a fixed cost of \$50,000 and the variable cost per unit is \$25. The revenue per unit was projected to be \$45, but a recent marketing study shows that because of an emerging competitor, the revenue will be about 12% lower. How does this affect the break-even point?

54) Administrators at a university will charge students \$150 to attend a seminar. It costs \$3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs \$25 per student for the administrators to provide the course materials. How many students would have to register for the seminar for the university to break even?

55) Administrators at a university are planning to offer a summer seminar. It costs \$3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs \$25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even?

56) Administrators at a university are planning to offer a summer seminar. It costs \$3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs \$25 per student for the administrators to provide the course materials. If 30 students pay \$175 for the privilege of attending the seminar, how much of a profit (or loss) will be incurred?

57) A newly opened bed-and-breakfast projects the following:
Monthly fixed costs \$8000
Variable cost per occupied room per night \$40
Revenue per occupied room per night \$165
Write the expression for total cost per month.

58) A newly opened bed-and-breakfast projects the following:
Monthly fixed costs \$8000
Variable cost per occupied room per night \$40
Revenue per occupied room per night \$165
Write the expression for total revenue per month.
Diff: 2 Page Ref: 8
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills

59) A newly opened bed-and-breakfast projects the following:
Monthly fixed costs \$8000
Variable cost per occupied room per night \$40
Revenue per occupied room per night \$165
How many rooms would have to be occupied per month in order to break even?

60) A script writer has received an advance against royalties of \$10,000. The royalty rate is \$2 for every performance in the U.S., and \$3 for every performance outside the U.S. Define variables for this problem.

61) A business analyst describes his company’s profit function as 3×2 + 6x – 200. If x is the output volume, what statements can you make about the price, fixed cost, and variable cost?

62) A script writer has received an advance against royalties of \$10,000. The royalty rate is \$2 for every performance in the U.S., and \$3 for every performance outside the U.S. Write an expression that could be used to compute the number of performances in order to cover the advance.

63) Students are organizing a “Battle of the Bands” contest. They know that at least 100 people will attend. The rental fee for the hall is \$150 and the winning band will receive \$500. In order to guarantee that they break even, how much should they charge for each ticket?

64) A popular performer is scheduled to appear at a major city. The promoter is deciding between two venues, the larger of which costs \$20,000 to rent and the smaller of which costs \$12,000 to rent. Ticket prices for the smaller venue are \$20, but the promoter is unsure what to charge per ticket for the larger venue. If exactly 1000 customers arrive, what percentage change in ticket prices would make the profit at the large venue identical to that of the smaller venue?

65) A manufacturer buys peas for vegetable pies from two cooperatives. The price per unit is \$6 from cooperative A and \$5.50 per unit from cooperative B. Define variables that would tell how many units to purchase from each source.

66) A manufacturer buys peas for vegetable pies from two cooperatives. The price per unit is \$6 from cooperative A and \$5.50 per unit from cooperative B. Develop an objective function that would minimize the total cost.

67) A manufacturer buys peas for vegetable pies from two cooperatives. The price per unit is \$6 from cooperative A and \$5.50 per unit from cooperative B. The manufacturer needs at least 12,000 units of peas. Cooperative A can supply up to 8000 units, and cooperative B can supply at least 6000 units. Develop constraints for these conditions.

68) A group of professors struggles to craft a set of assessment questions for their operations management intro class. They want to cover four topic areas with at least four questions each and have no more than twenty questions total for the assessment. What would a set of constraints look like if they chose an optimization approach to the assessment?

69) What are some different types of decision support systems?

70) A manager of the cereal bar at the college campus has determined that the profit made for each bowl of Morning Buzz cereal sold, x, is equal to: Z = \$4x – 0.5x. Each bowl of Morning Buzz weighs 6 ounces, and the manager has 12 lbs (192 ounces) of cereal available each day, which can be written as the constraint, 6x ≤ 192. What maximum profit will be made from Morning Buzz if it is all sold in one day?

71) The College Coffee Café buys tea from three suppliers. The price per pound is \$15.00 from supplier A, \$17.50 from supplier B, and \$21.00 from supplier C. They have budgeted \$175 to purchase the tea. The café needs at least 12 pounds of tea, and supplier C can supply no more than 4 pounds. Develop constraints for these conditions.

72) The College Coffee Café receives a profit of \$1.25 for each cup of house tea that they sell, \$1.40 for each cup of the premium brand, and \$1.50 for each cup of their special blend. Develop an objective that maximizes profit.

73) The steps of the management science process are:
A) problem definition, model construction, observation, model solution, implementation.
B) observation, problem definition, model construction, model solution, implementation.
C) model construction, problem definition, observation, model solution, implementation.
D) observation, implementation, problem definition, model construction, model solution.

74) A model is a functional relationship that includes:
A) variables.
B) parameters.
C) equations.
D) all of the above

75) Which of the following is an equation or an inequality that expresses a resource restriction in a mathematical model?
A) a decision variable
B) an objective function
C) a constraint
D) a parameter

76) There is considerable overlap in the scientific method and management science techniques. Which of the following steps is shared between them?
A) observation
B) problem definition
C) model construction
D) implementation

77) Which of the following is incorrect with respect to the use of models in decision making?
A) They improve understanding of the problem.
B) They promote subjectivity in decision making.
C) They are generally easy to use.
D) They provide a systematic approach to problem solving.
Diff: 3 Page Ref: 3
Section Heading: The Management Science Approach to Problem Solving
Keywords: model, problem solving
AACSB: Analytic skills
78) The field of management science
A) approaches decision making irrationally with techniques based on the scientific method.
B) is another name for management or human resources management.
C) concentrates on the use of quantitative methods to assist managers in decision making.
D) is completely separate and distinct from all other disciplines.
Diff: 1 Page Ref: 2
Section Heading: The Management Science Approach to Problem Solving
Keywords: management science, operations research
AACSB: Analytic skills

79) The processes of problem observation
A) cannot be done until alternatives are proposed.
B) requires consideration of multiple criteria.
C) is the first step of decision making.
D) is the final step of problem solving.
Diff: 1 Page Ref: 2
Section Heading: The Management Science Approach to Problem Solving
Keywords: observation, problem observation, management science process
AACSB: Analytic skills

80) The limits of the problem and the degree to which it pervades other units in the organization must be included during the ________ step of the management science process.
A) observation
B) definition
C) solution
D) implementation

81) ________ involves determining the functional relationship between variables, parameters, and equations.
A) Problem observation
B) Problem definition
C) Model construction
D) Model solution
Diff: 1 Page Ref: 3
Section Heading: The Management Science Approach to Problem Solving
Keywords: management science process, model construction
AACSB: Analytic skills

82) Which steps of the management science process can either be a recommended decision or information that helps a manager make a decision?
A) model implementation
B) problem definition
C) model solution
D) problem formulation
Diff: 2 Page Ref: 3
Section Heading: The Management Science Approach to Problem Solving
Keywords: management science process, model solution
AACSB: Analytic skills

83) The quantitative analysis approach requires
A) mathematical expressions for the relationship.
B) uncomplicated problems.
C) the manager to have prior experience with similar problems.
Diff: 2 Page Ref: 3
Section Heading: The Management Science Approach to Problem Solving
Keywords: management science, operations research, quantitative analysis
AACSB: Analytic skills

84) The earliest developments and use of management science techniques was in the field of
A) military operations.
C) politics.
D) manufacturing.
Diff: 2 Page Ref: 5
Section Heading: The Management Science Approach to Problem Solving
Keywords: management science, operations research
AACSB: Analytic skills
85) The result of an effective decision making process should be monitored in order to
A) reveal the break-even point.
B) reveal errors in the implementation.
C) keep fixed and variable costs distinct.
D) change the scientific method.
Diff: 2 Page Ref: 7
Section Heading: The Management Science Approach to Problem Solving
Keywords: decision making process
AACSB: Analytic skills

86) The management science process does not include
A) feedback.
B) implementation.
C) subjective preference.
D) information.
Diff: 2 Page Ref: 2
Section Heading: The Management Science Approach to Problem Solving
Keywords: management science process
AACSB: Analytic skills

87) The indicator that results in total revenues being equal to total cost is called the
A) marginal cost.
B) marginal volume.
C) break-even point.
D) profit mix.
Diff: 1 Page Ref: 7
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills

88) Variable cost
A) depends on the number of units produced.
B) plus marginal cost equals fixed cost.
C) is equal to total cost in deterministic models.
D) is the same as average cost.
Diff: 2 Page Ref: 7
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills
89) The components of break-even analysis are
A) cost and profit.
B) volume and cost.
C) volume, cost and profit.
D) volume and profit.
Diff: 1 Page Ref: 7
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills

90) ________ are generally independent of the volume of units produced and sold.
A) Fixed costs
B) Variable costs
C) Profits
D) Average cost
Diff: 1 Page Ref: 7
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills

91) The purpose of break-even analysis is to determine the number of units of a product to sell that will
A) appeal to the consumer.
B) result in a profit.
C) result in a loss.
D) result in zero profit.
Diff: 2 Page Ref: 7
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills

92) Variable cost does not include
A) raw materials and resources.
B) staff and management salaries.
C) material handling and freight.
D) direct labor and packaging.
Diff: 2 Page Ref: 7
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills
93) Which variable is not a component of break-even analysis?
A) fixed costs
B) variable costs
C) number of employees
D) number of customers
Diff: 1 Page Ref: 7
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills

94) At the break-even point,
A) total revenue equals total cost.
B) profit is maximized.
C) revenue is maximized.
D) costs are minimized.
Diff: 1 Page Ref: 9
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills

95) If the price increases, but fixed and variable costs do not change, the break-even point
A) decreases.
B) increases.
C) remains the same.
D) may increase or decrease, depending on sales.
Diff: 2 Page Ref: 10
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills

96) If the price decreases, but fixed and variable costs do not change, the break-even point
A) decreases
B) increases
C) remains the same
D) may increase or decrease, depending on sales
Diff: 2 Page Ref: 10
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills
97) The term ________ refers to testing how a problem solution reacts to changes in one or more of the model parameters.
A) graphical solution
B) decision analysis
C) sensitivity analysis
D) break-even analysis
Diff: 2 Page Ref: 10
Section Heading: Model Building: Break-Even Analysis
Keywords: sensitivity analysis, modeling process
AACSB: Analytic skills

98) If fixed costs decrease, but variable cost and price remain the same, the break-even point
A) decreases.
B) increases.
C) remains the same.
D) may increase or decrease depending on sales.
Diff: 2 Page Ref: 12
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills

99) If fixed costs increase, but variable cost and price remain the same, the break-even point
A) decreases.
B) increases.
C) remains the same.
D) may increase or decrease depending on sales.
Diff: 2 Page Ref: 12
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills
100) EKA manufacturing company produces part #2206 for the aerospace industry. Each unit of part #2206 is sold for \$15. The unit production cost of part #2206 is \$3. The fixed monthly cost of operating the production facility is \$3000. How many units of part #2206 have to be sold in a month to break even?
A) 166.67
B) 200
C) 250
D) 500
Diff: 2 Page Ref: 9
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills

101) EKA manufacturing company produces part #2206 for the aerospace industry. The unit production cost of part #2206 is \$3. The fixed monthly cost of operating the production facility is \$3000. Next month’s demand for part #2206 is 200 units. How much should the company charge for each unit of part #2206 to break even?
A) \$12
B) \$15
C) \$18
D) \$20
Diff: 2 Page Ref: 9
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills

102) A bed-and-breakfast breaks even every month if they book 30 rooms over the course of a month. Their fixed cost is \$6000 per month and the revenue they receive from each booked room is \$180. What is their variable cost per occupied room?
A) \$130
B) \$140
C) \$148
D) \$160
Diff: 3 Page Ref: 9
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills
103) Administrators at a university will charge students \$150 to attend a seminar. It costs \$3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs \$25 per student for the administrators to provide the course materials. How many students would have to register for the seminar for the university to break even?
A) 18
B) 20
C) 24
D) 30
Diff: 2 Page Ref: 9
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills

104) A university is planning a seminar. It costs \$3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs \$25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even?
A) \$120
B) \$150
C) \$175
D) \$200
Diff: 2 Page Ref: 9
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills

105) It costs \$50,000 to start a production process. Variable cost is \$25 per unit and revenue is \$45 per unit. What is the break-even point?
A) 1000 units
B) 1111 units
C) 2000 units
D) 2500 units
Diff: 1 Page Ref: 9
Section Heading: Model Building: Break-Even Analysis
Keywords: break-even analysis
AACSB: Analytic skills
106) Which of the following statements is false?
A) Decision models selectively describe the managerial situation.
B) Decision models consider all factors from the real world.
C) Decision models designate performance measures that reflect objectives.
D) Decision models designate decision variables.
Diff: 2 Page Ref: 3
Section Heading: The Management Science Approach to Problem Solving
Keywords: models, decision models, modeling techniques
AACSB: Analytic skills

107) Decision support systems and sensitivity analysis are useful management science tools for answering the question:
A) by when?
B) who else?
C) how much?
D) what if?
Diff: 2 Page Ref: 21
Section Heading: Management Science Models in Decision Support Systems
Keywords: decision support systems
AACSB: Analytic skills

108) A difficult aspect of using spreadsheets to solve management science problems is
A) obtaining the solution to standard management science problems.
B) data entry.
C) performing sensitivity analysis.
D) setting up a spreadsheet with complex models and formulas.
Diff: 2 Page Ref: 12
AACSB: Analytic skills

109) A technique that assumes certainty in its solution is referred to as
A) stochastic.
B) probabilistic.
C) deterministic.
D) parametric.
Diff: 2 Page Ref: 17
Section Heading: Management Science Modeling Techniques
Keywords: modeling, models, modeling techniques
AACSB: Analytic skills
110) Classification of management science techniques does not recognize
A) linear mathematical programming.
B) probabilistic techniques.
C) network techniques.
D) computer programming.
Diff: 1 Page Ref: 16
Section Heading: Management Science Modeling Techniques
Keywords: management science techniques, classification of techniques
AACSB: Analytic skills

111) Linear mathematical programming techniques assume that all parameters in the models are
A) known with certainty.
B) unknown.
C) predictable.
D) unpredictable.
Diff: 2 Page Ref: 16
Section Heading: Management Science Modeling Techniques
Keywords: management science techniques
AACSB: Analytic skills

112) Decision analysis is a ________ technique.
A) linear mathematical programming
B) probabilistic
C) network
D) non-linear programming technique
Diff: 1 Page Ref: 17
Section Heading: Management Science Modeling Techniques
Keywords: management science techniques
AACSB: Analytic skills

113) Which one of the following techniques is not a mathematical programming technique?
A) linear programming models
B) transportation models
C) analytical hierarchy process
D) integer linear programming technique
Diff: 2 Page Ref: 17
Section Heading: Management Science Modeling Techniques
Keywords: management science techniques
AACSB: Analytic skills
114) Which one of the following management science methods is not a probabilistic technique?
A) assignment models
B) decision analysis
C) queuing analysis
D) statistical analysis
Diff: 2 Page Ref: 17
Section Heading: Management Science Modeling Techniques
Keywords: management science techniques
AACSB: Analytic skills

115) A baker uses organic flour from a local farmer in all of his baked goods. For each batch of bread (x1), he uses 4 pounds of flour. For a batch of cookies (x2), he uses 3 pounds, and for a batch of muffins (x3) he uses 2 pounds. The local farmer can supply him with no more than 24 pounds per week. The constraint that represents this condition is:
A) x1 ≤ 8, x2 ≤ 8, x3 ≤ 8
B) x1 + x2 + x3 ≥ 24
C) x1 + x2 + x3 ≤ 24
D) 4×1 + 3×2 + 2×3 ≤ 24
Diff: 3 Page Ref: 16
Section Heading: Management Science Modeling Techniques
Keywords: constraints
AACSB: Analytic skills

116) An objective function
A) shows where the break-even point is.
B) describes how much of a resource can be used.
C) can represent costs or profits.
D) describes something to be maximized.
Diff: 2 Page Ref: 16
Section Heading: Management Science Modeling Techniques
Keywords: objective function, model construction
AACSB: Analytic skills

117) Larry’s Fish Market buys salmon (S) for \$5 per pound and a local whitefish (W) for \$3.50 per pound. Larry wants to minimize his cost, but he cannot spend more than \$160. The objective function that minimizes these costs for Larry is:
A) 5S + 3.5W ≤ 160
B) Min 5S + 3.5 W
C) Max 5S + 3.5 W
D) Min 5S + 3.5W ≥ 160
Diff: 3 Page Ref: 4
Section Heading: Management Science Modeling Techniques
Keywords: objective function, model construction
AACSB: Analytic skills

118) It’s time to buy pet food again and Lisa heads to the grocery store with \$40 in her purse, leaving her seven hungry cats and four hungry dogs at home. Dog food costs \$1 per can and cat food costs \$0.50 per can. Dogs eat two full cans of food each day but cats eat only one can. Lisa would like to buy enough food to last through her three-day weekend. What is an appropriate objective function for this scenario?
A) Min Z = 1D + 0.5C
B) Min Z = 2D + 1C
C) Min Z = D + C ≤ 40
D) Min Z = D + C ≥ 3
Diff: 3 Page Ref: 4
Section Heading: The Management Science Approach to Problem Solving
Keywords: objective function
AACSB: Analytic skills

119) It’s time to buy pet food again and Lisa heads to the grocery store with \$40 in her purse, leaving her seven hungry cats and four hungry dogs at home. Dog food costs \$1 per can and cat food costs \$0.50 per can. Dogs eat two full cans of food each day but cats eat only one can. Lisa would like to buy enough food to last through her three-day weekend. What is one appropriate constraint for this scenario?
A) 7C + 4D ≥ 3
B) 1C + 2D ≤ 40
C) .5C + 1D ≤ 40
D) 7C + 4D ≥ 1.5
Diff: 3 Page Ref: 4
Section Heading: The Management Science Approach to Problem Solving
Keywords: constraints
AACSB: Analytic skills

120) Marriott used which of the following management science techniques to help improve profit by \$120 million over two years?
A) optimization, decision analysis, and forecasting
B) forecasting, queuing theory, and inventory analysis
C) queuing theory, optimization, and inventory analysis
D) forecasting, simulation, and optimization
Diff: 3 Page Ref: 6
Section Heading: Management Science Modeling Techniques
Keywords: management science, management scientist
AACSB: Analytic skills

121) Which of these decision support systems is the most comprehensive with respect to an entire organization?
B) an ERP
C) QM for Windows
D) OLAP
Diff: 2 Page Ref: 20
Section Heading: Management Science Models in Decision Support Systems
Keywords: decision support systems
AACSB: Analytic skills

Introduction to Management Science, 11e (Taylor)
Chapter 11 Probability and Statistics

1) Deterministic techniques assume that no uncertainty exists in model parameters.
Diff: 1 Page Ref: 503
Keywords: deterministic techniques

2) Probabilistic techniques assume that no uncertainty exists in model parameters.
Diff: 1 Page Ref: 503
Keywords: probabilistic techniques

3) Objective probabilities that can be stated prior to the occurrence of an event are classical or a priori.
Diff: 2 Page Ref: 503
Keywords: objective probabilities, classical probabilities

4) Objective probabilities that are stated after the outcomes of an event have been observed are relative frequencies.
Diff: 2 Page Ref: 503
Keywords: relative frequencies

5) Relative frequency is the more widely used definition of objective probability.
Diff: 1 Page Ref: 504
Keywords: relative frequencies

6) Subjective probability is an estimate based on personal belief, experience, or knowledge of a situation.
Diff: 2 Page Ref: 504
Keywords: subjective probability
7) An experiment is an activity that results in one of several possible outcomes.
Diff: 1 Page Ref: 505
Keywords: experiment

8) The events in an experiment are mutually exclusive if only one can occur at a time.
Diff: 1 Page Ref: 505
Keywords: mutually exclusive events

9) In a given experiment, the probabilities of all mutually exclusive events sum to one.
Diff: 1 Page Ref: 505
Keywords: mutually exclusive events, rules of probability

10) A set of events is collectively exhaustive when it includes all the events that can occur in an experiment.
Diff: 2 Page Ref: 506
Keywords: collectively exhaustive events

11) A marginal probability is the probability of a single event occurring.
Diff: 1 Page Ref: 506
Keywords: marginal probability

12) A Venn diagram visually displays mutually exclusive and non-mutually exclusive events.
Diff: 2 Page Ref: 506
Keywords: Venn diagram

13) A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously.
Diff: 2 Page Ref: 506
Keywords: joint probability
14) A conditional probability is the probability that an event occurs given that another event has already occurred.
Diff: 1 Page Ref: 508
Section Heading: Statistical Independence and Dependence
Keywords: conditional probability

15) Conditional probabilities are shown in Venn diagrams.
Diff: 1 Page Ref: 506
Keywords: conditional probability

16) Probability trees are used only to compute conditional probabilities.
Diff: 2 Page Ref: 509
Section Heading: Statistical Independence and Dependence
Keywords: probability tree, conditional probability

17) A succession of events that does not affect other events is independent.
Diff: 1 Page Ref: 508
Section Heading: Statistical Independence and Dependence
Keywords: independence

18) A binomial probability distribution indicates the probability of r successes in n trials.
Diff: 2 Page Ref: 510
Section Heading: Statistical Independence and Dependence
Keywords: binomial probability distribution
AACSB: Analytic skills

19) A continuous random variable may assume only integer values within a given interval.
Diff: 1 Page Ref: 517
Keywords: continuous random variables
AACSB: Analytic skills

20) Seventy-two percent of all observations fall within one standard deviation of the mean if the data is normally distributed.
Diff: 1 Page Ref: 519
Keywords: normal distribution
AACSB: Analytic skills
21) Another name for the mean of a probability distribution is its expected value.
Diff: 1 Page Ref: 516
Keywords: expected value
AACSB: Analytic skills

22) The expected value of a discrete random variable is greater than or equal to zero.
Diff: 1 Page Ref: 516
Keywords: expected value

23) The variance of a discrete random variable is always greater than or equal to zero.
Diff: 1 Page Ref: 516
Keywords: expected value

24) The expected value of a random variable is computed by multiplying the sum of each possible value of the variable by the probability of that random variable.
Diff: 1 Page Ref: 516
Keywords: expected value
AACSB: Analytic skills

25) The variance of a random variable is computed by multiplying each possible value of the variable by its probability and summing these products.
Diff: 1 Page Ref: 516
Keywords: variance
AACSB: Analytic skills

26) For a typical normally distributed random variable, the standard deviation is equal to the variance.
Diff: 1 Page Ref: 518
Keywords: normal distribution
27) A normally distributed random variable has a mean of zero and a standard deviation of one.
Diff: 1 Page Ref: 517-518
Keywords: normal distribution

28) The standard normal distribution has a mean of one and a standard deviation of zero.
Diff: 1 Page Ref: 519
Keywords: standard normal distribution

29) The area under the normal curve represents probability.
Diff: 1 Page Ref: 518
Keywords: norm distrib, probability calculations with normal distribution

30) There is just as great a chance of a normally distributed random variable being over one standard deviation above the mean as there is being one standard deviation below the mean.
Diff: 1 Page Ref: 518
Keywords: norm distrib, probability calculations with normal distribution
AACSB: Analytic skills

31) An inspector correctly identifies defective products 90% of the time. For the next 10 products, the probability that he makes fewer than two incorrect inspections is 0.736.
Diff: 2 Page Ref: 510
Section Heading: Statistical Independence and Dependence
Keywords: binomial distribution
AACSB: Analytic skills

32) In Bayesian analysis, additional information is used to alter the conditional probability of the occurence of an event.
Diff: 1 Page Ref: 514
Section Heading: Statistical Independence and Dependence
Keywords: conditional probability

33) Objective probabilities that can be stated prior to the occurrence of an event are ________.
Diff: 1 Page Ref: 503
Keywords: probabilistic techniques, objective/classical probabilities
34) ________ probability is an estimate based on a personal belief, experience, and knowledge of a situation.

35) The events in an experiment are ________ if only one can occur at a time.

36) The term for including all possible events that can occur in an experiment is ________.

37) The cumulative probability for all six outcomes of tossing a fair die should end with the value ________.

38) The fact that the first toss of a coin has no effect on the outcome of the second toss of the coin suggests that these events are ________.

39) The collectively exhaustive set of events for flipping a coin is ________.

40) A ________ organizes numerical data to describe the events of an experiment.

41) A Venn diagram depicting two circles that do not overlap or touch in any way represents events that are ________.

42) A ________ is the probability of occurence of a single event.

43) ________ can enable one to improve marginal probabilities of the occurrence of an event by gathering additional information.

44) A succession of events that do not affect each other are ________.

45) A ________ probability is the probability that an event will occur given that another event has already occurred.

46) In a binomial distribution process, there are ________ possible outcomes.

47) One of the properties of the ________ distribution is that the probability of success remains constant over time.

48) Altered marginal probability of an event based on additional information is a ________ probability.

49) The ________ of a random variable is computed by multiplying each possible value of the variable by its probability and summing these products.

50) If events A and B are independent, then P(AB) = ________.

51) If events A and B are independent, then P(A|B) = ________.

52) If two events A and B are not mutually exclusive, then P(A or B) = ________.

53) ________ is a measure of dispersion of random variable values about the expected value.

54) A continuous random variable can take on a(n) ________ number of values within a given interval.

55) The ________ test is a statistical test to see if an observed data fit a particular probability distribution.

56) The ________ normal distribution has a mean of 0 and a standard deviation of 1.

57) Almost all of the data from a normal distribution fall within ________ standard deviations of the mean.

58) The expected value of the standard normal distribution is equal to ________.

59) The standard deviation of the standard normal distribution is equal to ________.
Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y.

60) What is the probability that Jim will be accepted at both universities?

61) What is the probability that Jim will not be accepted at either university?

62) What is the probability that Jim will be accepted by at least one of the two universities?

Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category.

Male (M) Female (F)
Job
Salaried staff (SS) 30 50
Hourly staff (HS) 60 40

63) If an employee is selected at random, what is the probability that the employee is male?

64) If an employee is selected at random, what is the probability that the employee is male and salaried staff?

65) If an employee is selected at random, what is the probability that the employee is female given that the employee is a salaried staff member?

66) If an employee is selected at random, what is the probability that the employee is female or works as a member of the administration

The Dean’s Office keeps tracks of student complaints received each week. The probability distribution for complaints can be represented as a table as shown below. The random variable xi represents the number of complaints, and p(xi) is the probability of receiving xi complaints.

0 1 2 3 4 5 6
p( ) .10 .15 .18 .20 .20 .10 .07

67) What is the probability that they receive less than 3 complaints in a week?

68) What is the average number of complaints received per week?

69) A fair die is rolled nine times. What is the probability that an odd number (1, 3, or 5) will occur less than 3 times?

70) A fair die is rolled 8 times. What is the probability that an even number (2, 4, or 6) will occur between 2 and 4 times?

A company markets educational software products, and is ready to place three new products on the market. Past experience has shown that for this particular software, the chance of “success” is 80%. Assume that the probability of success is independent for each product.

71) Find the probability that exactly 1 of the 3 products is successful.

72) Find the probability that none of the 3 products is successful.

73) If X has the following probability distribution

X 1 2 3 4
P(X) .1 .5 .2 .2

Compute the expected value of X.

74) Assume X has the following probability distribution :

X 1 2 3 4
P(X) .1 .5 .2 .2

Compute the standard deviation of X.

75) If x is normally distributed with a mean of 10 and a standard deviation of 3, then P(x ≤ 6) is equal to P( Z ≤ _____)?

76) For a standard normal distribution, what is the probability that z is greater than 1.75?

Two psychology majors, in two different sections of Clinical Psychology, were comparing test scores. The following gives the students’ scores, class mean, and standard deviation for each section:

Section 1 Section 2
Student score 84 75
Mean 75 60
Standard deviation 7 8

77) What is the z-score of the student from section 1 and what is the probability that a student in section 1 will score higher than 84?

78) What is the z-score of the student from section 2 and what is the probability that a student in section 2 will score higher than 75?

79) Which student scored better compared to the rest of their section?

80) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is larger than 21 oz?

81) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf of bread is larger than 23 oz?

82) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is less than 24 oz?

83) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is between 20.75 and 23.25 oz?

84) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is between 21.75 and 22.25 oz?

85) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is more than 24 oz?

86) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is more than 22.25 oz?

87) A life insurance company wants to estimate its annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the plan recipients would receive payments beyond age 75?

88) A life insurance company wants to estimate its annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the participants die before they reach the age of 65?

89) A life insurance company wants to estimate its annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. By what age have 80% of the plan participants passed away?

90) For the normal distribution, the mean plus and minus 1.96 standard deviations will include what percent of the observations?

91) What is the area under the normal curve for Z ≥ 1.79?

92) A study of a company’s practice regarding the payment of invoices revealed that on the average an invoice was paid 20 days after it was received. The standard deviation equaled 5 days. Assuming that the distribution is normal, what percent of the invoices is paid within 15 days of receipt?

93) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. Assuming the weights of the crabs are normally distributed, what is the probability that a randomly selected crab will weigh more than 2.2 pounds?

94) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. Assuming the weights of crabs are normally distributed, what is the probability that a randomly selected crab will weigh between 1 and 2 pounds?

95) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. Assuming the weights of crabs are normally distributed, the probability that a randomly selected crab will weigh less than 1.2 pounds is ________.

96) A research scientist has observed the monkeys of the Nandi Hills outside of Bangalore for the last twenty years, carefully cataloging their preferences for a number of food items. An unsuspecting tourist leaves his can of soda unattended. Describe the type of probability the research scientist can assign to the likelihood that the soda will become the monkey’s next meal. Then contrast this type of probability with the other of the two basic types.

97) What are the differences between deterministic and probabilistic techniques?

Horatio Oscar Vineeth Lane (HOV Lane for short) records his commute times for a period of one month and assigned them to five different categories as shown in the table.

Commute Length Number of Observations
commute time <10 minutes 1
10 ≤ commute time < 20 minutes 2
20 ≤ commute time < 30 minutes 4
30 ≤ commute time < 40 minutes 9
40 ≤ commute time < 50 minutes 4

98) What is the likelihood that the commute will take 30 minutes or longer?
Diff: 1 Page Ref: 508
Keywords: cumulative probability distribution
AACSB: Analytic skills

99) What is the cumulative probability for the three shortest commute categories?

100) What is the average commute time for HOV Lane?

101) Assume that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2. Find the probability that X is between 48 and 55.

102) A paint manufacturer’s production process is normally distributed with a mean of 100,000 gallons and a standard deviation of 10,000 gallons. Management wants to create an incentive bonus for the production crew when the daily production exceeds the 94th percentile of the distribution. At what level of production should management pay the incentive bonus?

An online sweepstakes has the following payoffs and probabilities. Each person is limited to one entry.

103) The probability that someone wins any money is ________.

104) The probability of winning at least \$1000 is ________.

105) ________ techniques assume that no uncertainty exists in model parameters.
A) Probability
B) Probabilistic
C) Deterministic
D) Distribution

106) ________ probability is an estimate based on personal belief, experience, or knowledge of a situation.
A) Binomial
B) Subjective
C) Marginal
D) Joint
Diff: 2 Page Ref: 504
Keywords: subjective probability

107) Objective probabilities that can be stated prior to the occurrence of an event are
A) deterministic or probabilistic.
B) subjective or objective.
C) classical or a priori.
D) relative or subjective.
Diff: 2 Page Ref: 503
Keywords: classical (or a priori) probability

108) The events in an experiment are ________ if only one can occur at a time.
A) mutually exclusive
B) non-mutually exclusive
C) mutually inclusive
D) independent
Diff: 1 Page Ref: 505
Keywords: mutually exclusive events

109) In a given experiment the probabilities of mutually exclusive events sum to:
A) 0
B) 0.5
C) 1
D) This cannot be answered without knowing the probability values of the events.
Diff: 1 Page Ref: 505
Keywords: mutually exclusive events
110) A ________ probability is the probability of a single event occurring.
A) subjective
B) binomial
C) marginal
D) joint
Diff: 1 Page Ref: 506
Keywords: marginal probability

111) A frequency distribution is an organization of ________ data about the events in an experiment.
A) quantitative
B) integer
C) qualitative
D) unknown
Diff: 1 Page Ref: 505
Keywords: frequency distribution

112) Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. What is the probability that Jim will be accepted at both universities?
A) .65
B) .25
C) .20
D) .09
Diff: 2 Page Ref: 505
Keywords: multiplication of probabilities
AACSB: Analytic skills
113) Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. What is the probability that Jim will not be accepted at either university?
A) .30
B) .36
C) .44
D) .56
Diff: 2 Page Ref: 506
Keywords: multiplication of probabilities
AACSB: Analytic skills

114) Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category.

Male (M) Female (F)
Job
Salaried staff (SS) 30 50
Hourly staff (HS) 60 40

If an employee is selected at random, what is the probability that the employee is female or works as a member of the administration?
A) .17
B) .67
C) .70
D) .73
Diff: 2 Page Ref: 508
Keywords: not mutually exclusive events, addition rule
AACSB: Analytic skills

115) A ________ probability distribution indicates the probability of r successes in n trials.
A) joint
B) subjective
C) marginal
D) binomial
Diff: 2 Page Ref: 510
Section Heading: Statistical Independence and Dependence
Keywords: binomial probability distribution
116) The probability of independent events occurring in succession is computed by ________ the probabilities of each event.
A) multiplying
C) subtracting
D) dividing
Diff: 2 Page Ref: 508
Section Heading: Statistical Independence and Dependence
Keywords: independent events

117) A ________ probability is the probability that an event will occur given that another event has already occurred.
A) subjective
B) objective
C) conditional
D) binomial
Diff: 2 Page Ref: 508
Section Heading: Statistical Independence and Dependence
Keywords: conditional probability

118) In Bayesian analysis, additional information is used to alter the ________ probability of the occurrence of an event.
A) marginal
B) conditional
C) binomial
D) revised
Diff: 2 Page Ref: 514
Section Heading: Statistical Independence and Dependence
Keywords: marginal probability

119) Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category.

Male (M) Female (F)
Job
Salaried staff (SS) 30 50
Hourly staff (HS) 60 40

If an employee is selected at random, what is the probability that the employee is female given that the employee is a salaried staff member?
A) .50
B) .60
C) .625
D) .70
Diff: 2 Page Ref: 510
Section Heading: Statistical Independence and Dependence
Keywords: conditional probability
AACSB: Analytic skills

120) A ________ probability is the altered marginal probability of an event based on additional information.
A) posterior
B) joint
C) marginal
D) conditional
Diff: 2 Page Ref: 514
Section Heading: Statistical Independence and Dependence
Keywords: posterior (revised) probability

121) Mutually exclusive events are
A) events with identical probabilities.
B) events that have no outcomes in common.
C) events that have no effect on each other.
D) events that are represented in a Venn diagram by two overlapping circles.
Diff: 2 Page Ref: 505
Keywords: mutually exclusive events

122) Bayesian analysis involves a(n) ________ probability.
A) a priori
B) posterior
C) joint
D) relative frequency
Diff: 2 Page Ref: 514
Section Heading: Statistical Independence and Dependence
Keywords: Bayesian analysis

123) In a ________ distribution, for each of n trials, the event always has the same probability of occurring.
A) binomial
B) joint
C) frequency
D) standard
Diff: 2 Page Ref: 510
Section Heading: Statistical Independence and Dependence
Keywords: binomial distribution

124) Experiments with repeated independent trials will be described by the binomial distribution if
A) each trial result influences the next.
B) each trial has exactly two outcomes whose probabilities do not change.
C) the trials are continuous.
D) the time between trials is constant.
Diff: 2 Page Ref: 510
Section Heading: Statistical Independence and Dependence
Keywords: binomial distribution

125) In a binomial distribution, for each of n trials, the event
A) time between trials is constant.
B) always has the same probability of occurring.
C) result of the first trial influence the next trial.
D) trials are continuous.
Diff: 2 Page Ref: 510
Section Heading: Statistical Independence and Dependence
Keywords: binomial distribution

126) A fair die is rolled nine times. What is the probability that an odd number (1, 3, or 5) will occur less than 3 times?
A) .0899
B) .2544
C) .7456
D) .9101
Diff: 2 Page Ref: 510
Section Heading: Statistical Independence and Dependence
Keywords: binomial distribution
AACSB: Analytic skills

127) A fair die is rolled 8 times. What is the probability that an even number (2, 4, or 6) will occur between 2 and 4 times?
A) .2188
B) .4922
C) .6016
D) .8204
Diff: 2 Page Ref: 510
Section Heading: Statistical Independence and Dependence
Keywords: binomial distribution
AACSB: Analytic skills

128) A company markets educational software products and is ready to place three new products on the market. Past experience has shown that for this particular software, the chance of “success” is 80%. Assume that the probability of success is independent for each product. What is the probability that exactly 1 of the 3 products is successful?
A) 0.80
B) 0.032
C) 0.24
D) 0.096
Diff: 2 Page Ref: 510
Section Heading: Statistical Independence and Dependence
Keywords: binomial distribution
AACSB: Analytic skills
129) ________ is a measure of the dispersion of random variable values about the expected value or mean.
A) Standard deviation
B) Sample mean
C) Population mean
D) Expected value
Diff: 2 Page Ref: 515
Keywords: variance, standard deviation

130) An automotive center keeps tracks of customer complaints received each week. The probability distribution for complaints can be represented as the table shown below. The random variable xi represents the number of complaints, and p(xi) is the probability of receiving xi complaints.

0 1 2 3 4 5 6
p( ) .10 .15 .18 .20 .20 .10 .07

What is the average number of complaints received per week?
A) 2.12
B) 3.32
C) 4.12
D) 2.83
Diff: 2 Page Ref: 516
Keywords: expected value
AACSB: Analytic skills

131) The expected value of the standard normal distribution is equal to:
A) 0
B) 1
C) 1.5
D) 2
Diff: 1 Page Ref: 519
Keywords: expected value
132) The area under the normal curve represents probability, and the total area under the curve sums to:
A) 0
B) 0.5
C) 1
D) 2
Diff: 2 Page Ref: 517
Keywords: normal distribution

133) The ________ and variance are derived from a subset of the population data and are used to make inferences about the population.
A) population variance
B) population standard deviation
C) population mean
D) sample mean
Diff: 1 Page Ref: 511
Keywords: mean and variance

134) Under the normal curve, the area between z = 1 and z = -2 includes approximately ________ of the values.
A) 98%
B) 95%
C) 85%
D) 82%
Diff: 3 Page Ref: 520
Keywords: normal distribution
AACSB: Analytic skills

135) For the normal distribution, the mean plus and minus 1.96 standard deviations will include what percent of the observations?
A) 84%
B) 90%
C) 95%
D) 97%
Diff: 1 Page Ref: 520
Keywords: normal distribution
AACSB: Analytic skills
136) The weight of a jar of jelly is normally distributed with a mean of 16 oz and a standard deviation of 0.02 oz. What is the probability that a jar of jelly contains less than 16 oz?
A) .1915
B) .3085
C) .5000
D) .7257
Diff: 2 Page Ref: 520
Keywords: norm distrib, probability calculations with normal distribution
AACSB: Analytic skills

137) The weight of a jar of jelly is normally distributed with a mean of 16 oz and a standard deviation of 0.02 oz. What is the probability that a jar of jelly contains more than 16.03 oz?
A) .0668
B) .1587
C) .4332
D) .9332
Diff: 2 Page Ref: 519
Keywords: norm distrib, probability calculations with normal distribution
AACSB: Analytic skills

138) Under the normal curve, the area between z = 2 and z = -2 includes ________ of the values.
A) 98%
B) 96%
C) 95%
D) 93%
Diff: 2 Page Ref: 519
Keywords: normal distribution
AACSB: Analytic skills
139) The metropolitan airport commission is considering the establishment of limitations on noise pollution around a local airport. At the present time, the noise level per jet takeoff in one neighborhood near the airport is approximately normally distributed with a mean of 100 decibels and a standard deviation of 3 decibels. What is the probability that a randomly selected jet will generate a noise level of more than 105 decibels?
A) 0.0228
B) 0.0475
C) 0.0485
D) 0.0500
Diff: 2 Page Ref: 520
Keywords: normal distribution
AACSB: Analytic skills

140) For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.2910. The value of Z is:
A) 0.17
B) 0.81
C) 1.25
D) 1.65
Diff: 2 Page Ref: 520
Keywords: normal distribution
AACSB: Analytic skills

141) For some value of Z, the probability that a standard normal variable is below Z is 0.3783. The value of Z is:
A) -0.81
B) -0.31
C) 0.82
D) 1.55
Diff: 2 Page Ref: 519
Keywords: standard normal distribution
AACSB: Analytic skills
142) For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3554. The value of Z is:
A) 0.31
B) 0.36
C) 0.95
D) 1.06
Diff: 2 Page Ref: 519
Keywords: norm distrib, probability calculations with normal distribution
AACSB: Analytic skills

143) If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.
A) 0.3551
B) 0.3085
C) 0.2674
D) 0.1915
Diff: 1 Page Ref: 520
Keywords: normal distribution
AACSB: Analytic skills

144) Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. Find the probability that a randomly selected college student will take between 2 and 6 minutes to find a parking spot in the main parking lot.
A) 0.1950
B) 0.4772
C) 0.4332
D) 0.6247
Diff: 1 Page Ref: 520
Keywords: norm distrib, probability calculations with normal distribution
AACSB: Analytic skills

145) Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. What time is exceeded by approximately 75% of the college students when trying to find a parking spot in the main parking lot?
A) 3.65 minutes
B) 5.75 minutes
C) 6.36 minutes
D) 9.21 minutes
Diff: 2 Page Ref: 519
Keywords: normal distribution
AACSB: Analytic skills

146) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. What weight is exceeded by 2% of all of the crabs? (Assume the weights are normally distributed.)
A) 0.78 pounds
B) 1.82 pounds
C) 2.42 pounds
D) 4.36 pounds
Diff: 2 Page Ref: 520
Keywords: norm distrib, probability calculations with normal distribution
AACSB: Analytic skills

147) A professor would like to assign grades such that 5% of students receive As. If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an A? (Round your answer.)
A) 80
B) 83
C) 90
D) 93
Diff: 2 Page Ref: 520
Keywords: norm distrib, probability calculations with normal distribution
AACSB: Analytic skills
148) A professor would like to assign grades such that 7% of students receive Fs. If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an F? (Round your answer.)
A) 43
B) 49
C) 50
D) 55
Diff: 2 Page Ref: 519
Keywords: norm distrib, probability calculations with normal distribution
AACSB: Analytic skills

Horatio Oscar Vineeth Lane (HOV Lane for short) records his commute times for a period of one month and assigned them to five different categories as shown in the table.

Commute Length Number of Observations
commute time <10 minutes 1
10 ≤ commute time < 20 minutes 2
20 ≤ commute time < 30 minutes 4
30 ≤ commute time < 40 minutes 9
40 ≤ commute time < 50 minutes 4

149) What is the duration of Mr. Lane’s expected commute?
A) 31.5 minutes
B) 27.25 minutes
C) 25.5 minutes
D) 33.75 minutes
Diff: 2 Page Ref: 516
Keywords: expected value
AACSB: Analytic skills

150) What is the probability that Mr. Lane makes it home in under thirty minutes?
A) .15
B) .35
C) .20
D) .55
Diff: 2 Page Ref: 507-508
Keywords: cumulative probability distribution
AACSB: Analytic skills
151) What kind of probability is demonstrated if Mr. Lane is asked to predict the duration of his next commute?
A) subjective probability
B) conjecture probability
C) objective probability
D) reflexive probability
Diff: 2 Page Ref: 503
Keywords: objective probabilities, classical probabilities

152) Which of these events are mutually exclusive?
A) The duration of Mr. Lane’s commute is less than expected; Mr. Lane’s commute is between twenty and thirty minutes.
B) Mr. Lane’s commute is longer than 30 minutes; Mr. Lane’s commute is longer than 40 minutes.
C) Mr Lanes commute is between ten and forty minutes; Mr. Lane’s commute is between twenty and thirty minutes.
D) Mr. Lane’s commute takes less than ten minutes; Mr Lane’s commute exceeds his expected commute.
Diff: 1 Page Ref: 506
Keywords: mutually exclusive events

Strayer Mat 540 Quiz 1 Solution
Mat540 Quiz 1 Solved
Mat540 Week 2 Quiz
MAT 540 Quiz chapter 1 chapter 11
Week 2 Quiz mat 540 solved
Mat 540 quantitative methods quiz 1
Mat 540, quiz, q, week, chapter, 1, 11, 2, solution, strayer university

# MAT 540 Week 8 Homework Problems – Strayer University New

MAT/540 Week 8 Problems Chapter 4 Solution

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MAT 540 Week 8 Chapter 4 Problems

Chapter 4

14 Grafton Metalworks Company produces metal alloys from six different ores it mines. The company has an order from a customer to produce an alloy that contains four metals according to the following specifications: at least 21% of metal A, no more than 12% of metal B, no more than 7% of metal C and between 30% and 65% of metal D. The proportion of the four metals in each of the six ores and the level of impurities in each ore are provided in the following table:

Ore Metal (%) Impurities (%) Cost/Ton
A B C D
1 19 15 12 14 40 27
2 43 10 25 7 15 25
3 17 0 0 53 30 32
4 20 12 0 18 50 22
5 0 24 10 31 35 20
6 12 18 16 25 29 24

When the metals are processed and refined, the impurities are removed.

The company wants to know the amount of each ore to use per ton of the alloy that will minimize the cost per ton of the alloy.

1. Formulate a linear programming model for this problem.
2. Solve the model by using the computer.

19 As a result of a recently passed bill, a congressman’s district has been allocated \$4 million for programs and projects. It is up to the congressman to decide how to distribute the money. The congressman has decided to allocate the money to four ongoing programs because of their importance to his district – a job training program, a parks project, a sanitation project, and a mobile library. However, the congressman wants to distribute the money in a manner that will please the most voters, or, in other words, gain him the most votes in the upcoming election. His staff’s estimates of the number of votes gained per dollar spent for the various programs are as follows.

Job training 0.02
Parks 0.09
Sanitation 0.06
Mobile library 0.04

In order also to satisfy several local influential citizens who financed his election, he is obligated to observe the following guidelines:

• None of the programs can receive more than 40% of the total allocation.

• The amount allocated to parks cannot exceed the total allocated to both the sanitation project and the mobile library
• The amount allocated to job training must at least equal the amount spent on the sanitation project.

Any money not spent in the district will be returned to the government; therefore, the congressman wants to spend it all. The congressman wants to know the amount to allocate to each program to maximize his votes.

1. Formulate a linear programming model for this problem.
2. Solve the model by using the computer.

20 Anna Broderick is the dietician for the State University football team, and she is attempting to determine a nutritious lunch menu for the team. She has set the following nutritional guidelines for each lunch serving:

• Between 1,500 and 2,000 calories
• At least 5 mg of iron
• At least 20 but no more than 60 g of fat
• At least 30 g of protein
• At least 40 g of carbohydrates
• No more than 30 mg of cholesterol

She selects the menu from seven basic food items, as follows, with the nutritional contributions per pound and the cost as given:

Calories
(per lb.) Iron
(mg/lb.) Protein
(g/lb.) Carbo-hydrates
(g/lb.) Fat (g/lb.) Chol-esterol
(mg/lb.) Cost

\$/lb.
Chicken 520 4.4 17 0 30 180 0.80
Fish 500 3.3 85 0 5 90 3.70
Ground beef 860 0.3 82 0 75 350 2.30
Dried beans 600 3.4 10 30 3 0 0.90
Lettuce 50 0.5 6 0 0 0 0.75
Potatoes 460 2.2 10 70 0 0 0.40
Milk (2%) 240 0.2 16 22 10 20 0.83

The dietician wants to select a menu to meet the nutritional guidelines while minimizing the total cost per serving.

1. Formulate a linear programming model for this problem.
2. Solve the model by using the computer
3. If a serving of each of the food items (other than milk) was limited to no more than a half pound, what effect would this have on the solution?

22 The Cabin Creek Coal (CCC) Company operates three mines in Kentucky and West Virginia, and it supplies coal to four utility power plants along the East Coast. The cost of shipping coal from each mine to each plant, the capacity at each of the three mines and the demand at each plant are shown in the following table:

Plant
Mine 1 2 3 4 Mine Capacity (tons)
1 \$ 7 \$ 9 \$10 \$12 220
2 9 7 8 12 170
3 11 14 5 7 280
Demand (tons) 110 160 90 180

The cost of mining and processing coal is \$62 per ton at mine 1, \$67 per ton at mine 2, and \$75 per ton at mine 3. The percentage of ash and sulfur content per ton of coal at each mine is as follows:

Mine % Ash % Sulfur
1 9 6
2 5 4
3 4 3

Each plant has different cleaning equipment. Plant 1 requires that the coal it receives have no more than 6% ash and 5% sulfur; plant 2 coal can have no more than 5% ash and sulfur combined; plant 3 can have no more than 5% ash and 7% sulfur; and plant 4 can have no more than 6% ash and sulfur combined. CCC wabts to determine the amount of coal to produce at each mine and ship to its customers that will minimize its total cost.

1. Formulate a linear programming model for this problem.
2. Solve this model by using the computer.

36 Joe Henderson runs a small metal parts shop. The shop contains three machines – a drill press, a lathe, and a grinder. Joe has three operators, each certified to work on all three machines. However, each operator performs better on some machines than on others. The shop has contracted to do a big job that requires all three machines. The times required by the various operators to perform the required operations on each machine are summarized as follows:

Operator Drill Press (min) Lathe (min) Grinder (min)
1 23 18 35
2 41 30 28
3 25 36 18

Joe Henderson wants to assign one operator to each machine so that the topal operating time for all three operators is minimized.

1. Formulate a linear programming model for this problem.
2. Solve the model by using the computer
3. Joe’s brother, Fred, has asked him to hire his wife, Kelly, who is a machine operator. Kelly can perform each of the three required machine operations in 20 minutes. Should Joe hire his sister-in-law?

43 The Cash and Carry Building Supply Company has received the following order for boards in three lengths:

Length Order (quantity)
7 ft. 700
9 ft. 1,200
10 ft. 300

The company has 25-foot standard-length boards in stock. Therefore, the standard-length boards must be cut into the lengths necessary to meet order requirements. Naturally, the company wishes to minimize the number of standard-length boards used.

1. Formulate a linear programming model for this problem.
2. Solve the model by using the computer
3. When a board is cut in a specific pattern, the amount of board left over is referred to as “trim-loss.” Reformulate the linear programming model for this problem, assuming that the objective is to minimize trim loss rather than to minimize the total number of boards used, and solve the model. How does this affect the solution?

# MAT 540 Week 7 Homework Problems – Strayer University New

MAT 540 Week 7 Homework Problems Chapter 3 Solution

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MAT 540 Chapter 3 Homework Problems

Chapter 3
8. Solve the model formulated in Problem 7 for Southern Sporting Goods Company using the computer.
a. State the optimal solution.
b. What would be the effect on the optimal solution if the profit for a basketball changed from \$12 to \$13? What would be the effect if the profit for a football changed from \$16 to \$15?
c. What would be the effect on the optimal solution if 500 additional pounds of rubber could be obtained? What would be the effect if 500 additional square feet of leather could be obtained? Reference Problem 7. Southern Sporting Good Company makes basketballs and footballs. Each product is produced from two resources rubber and leather. The resource requirements for each product and the total resources available are as follows: Resource Requirements per Unit Product Rubber (lb.) Leather (ft2) Basketball 3 4 Football 2 5 Total resources available 500 lb. 800 ft2
10. A company produces two products, A and B, which have profits of \$9 and \$7, respectively. Each unit of product must be processed on two assembly lines, where the required production times are as follows: Hours/ Unit Product Line 1 Line2 A 12 4 B 4 8 Total Hours 60 40 a. Formulate a linear programming model to determine the optimal product mix that will maximize profit. b. Transform this model into standard form.
11. Solve problem 10 using the computer.
a. State the optimal solution.
b. What would be the effect on the optimal solution if the production time on line 1 was reduced to 40 hours?
c. What would be the effect on the optimal solution if the profit for product B was increased from \$7 to \$15 to \$20?
12. For the linear programming model formulated in Problem 10 and solved in Problem 11.
a. What are the sensitivity ranges for the objective function coefficients?
b. Determine the shadow prices for additional hours of production time on line 1 and line 2 and indicate whether the company would prefer additional line 1 or line 2 hours.
14. Solve the model formulated in Problem 13 for Irwin Textile Mills. a. How much extra cotton and processing time are left over at the optimal solution? Is the demand for corduroy met? b. What is the effect on the optimal solution if the profit per yard of denim is increased from \$2.25 to \$3.00? What is the effect if the profit per yard of corduroy is increased from \$3.10 to \$4.00? c. What would be the effect on the optimal solution if Irwin Mils could obtain only 6,000 pounds of cotton per month? Reference Problem 13. Irwin Textile Mills produces two types of cotton cloth – denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such, requires 7.5 pounds of raw cotton per yard, whereas denim requires 5 pounds of raw cotton per yard. A yard of corduroy requires 3.2 hours of processing time; a yard of denim requires 3.0 hours. Although the demand for denim is practically unlimited, the maximum demand for corduroy is 510 yards per month. The manufacturer has 6,500 pounds of cotton and 3,000 hours of processing time available each month. The manufacturer makes a profit of \$2.25 per yard of denim and \$3.10 per yard of corduroy. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit. Formulate the model and put it into standard form. Solve it.
15. Continuing the model from Problem 14. a. If Irwin Mills can obtain additional cotton or processing time, but not both, which should it select? How much? Explain your answer. b. Identify the sensitivity ranges for the objective function coefficients and for the constraint quantity values. Then explain the sensitivity range for the demand for corduroy.
16. United Aluminum Company of Cincinnati produces three grades (high, medium, and low) of aluminum at two mills. Each mill has a different production capacity (in tons per day) for each grade as follows: Aluminum Grade Mill 1 2 High 6 2 Medium 2 2 Low 4 10 The company has contracted with a manufacturing firm to supply at least 12 tons of high-grade aluminum, and 5 tons of low-grade aluminum. It costs United \$6,000 per day to operate mill 1 and \$7,000 per day to operate mill 2. The company wants to know the number of days to operate each mill in order to meet the contract at minimum cost. a. Formulate a linear programming model for this problem.
18. Solve the linear programming model formulated in Problem 16 for Unite Aluminum Company by using the computer. a. Identify and explain the shadow prices for each of the aluminum grade contract requirements. b. Identify the sensitivity ranges for the objective function coefficients and the constraint quantity values. c. Would the solution values change if the contract requirements for high-grade alumimum were increased from 12 tons to 20 tons? If yes, what would the new solution values be?
24. Solve the linear programming model developed in Problem 22 for the Burger Doodle restaurant by using the computer. a. Identify and explain the shadow prices for each of the resource constraints b. Which of the resources constrains profit the most? c. Identify the sensitivity ranges for the profit of a sausage biscuit and the amount of sausage available. Explain these sensitivity ranges. Reference Problem 22. The manager of a Burger Doodle franchise wants to determine how many sausage biscuits and ham biscuits to prepare each morning for breakfast customers. The two types of biscuits require the following resources: Biscuit Labor (hr.) Sausage (lb.) Ham (lb.) Flour (lb.) Sausage 0.010 0.10 — 0.04 Ham 0.024 — 0.15 0.04 The franchise has 6 hours of labor available each morning. The manager has a contract with a local grocer for 30 pounds of sausage and 30 pounds of ham each morning. The manager also purchases 16 pounds of flour. The profit for a sausage biscuit is \$0.60; the profit for a ham biscuit is \$0.50. The manager wants to know the number of each type of biscuit to prepare each morning in order to maximize profit. Formulate a linear programming model for this problem.

# MAT 540 Week 6 Homework Problems – Strayer University New

MAT 540 Week 6 Homework Problems Chapter 2

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MAT 540 Chapter 2 Homework Problems Solution

Complete the following problems from Chapter 2:
• Problems 2, 6, 7, 12, 16, 20
• Homework
• Chapter 2

2. A company produces two products that are processed on two assembly lines. Assembly line 1 has 100 available hours, and assembly line 2 has 42 available hours. Each product requires 10 hours of processing time on line 1, while on line 2 product 1 requires 7 hours and product 2 requires 3 hours. The profit for product 1 is \$6 per unit, and the profit for product 2 is \$4 per unit.
a. Formulate a linear programming model for this problem.
b. Solve the model by using graphical analysis.

6. The Pinewood Furniture Company produces chairs and tables from two resources – labor and wood. The company has 80 hours of labor and 36 board-ft. of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 board-ft. of wood, whereas a table requires 10 hours of labor and 6 board-ft. of wood. The profit derived from each chair is \$400 and from each table, \$100. The company wants to determine the number of chairs and tables to produce each day in order to maximize profit. Formulate a linear programming model for this problem.
a. Formulate a linear programming model for this problem.
b. Solve the model by using graphical analysis.

7. In Problem 6, how much labor and wood will be unused if the optimal numbers of chairs and tables are produced?

12. The Elixer Drug Company produces a drug from two ingredients. Each ingredient contains the same three antibiotics, in different proportions. One gram of ingredient 1 contributes 3 units and one gram of ingredient 2 contributes 1 unit of antibiotic 1; the drug requires 6 units. At least 4 units of antibiotic 2 are required and the ingredients contribute 1 unit each per gram. At least 12 units of antibiotic 3 are required; a gram of ingredient 1 contributes 2 units, and a gram of ingredient 2 contributes 6 units. The cost for a gram of ingredient 1 is \$80, and the cost for a gram of ingredient 2 is \$50. The company wants to formulate a linear programming model to determine the number of grams of each ingredient that must go into the drug in order to meet the antibiotic requirements at the minimum cost.
a. Formulate a linear programming model for this problem.
b. Solve the model by using graphical analysis.

16. A clothier makes coats and slacks. The two resources required are wool cloth and labor. The clothier has 150 square yards of wool and 200 hours of labor available. Each coat requires 3 square yards of wool and 10 hours of labor, whereas each pair of slacks requires 5 square yards of wool and 4 hours of labor. The profit for a coat is \$50, and the profit for slacks is \$40. The clothier wants to determine the number of coats and pairs of slacks to make so that profit will be maximized.
a. Formulate a linear programming model for this problem.
b. Solve the model by using graphical analysis.

20. Solve the following linear programming model graphically:
Maximize Z = 5×1 + 8×2

Subject to
3×1 + 5×2 ≤ 50
2×1 + 4×2 ≤ 40
x1 ≤ 8
x2 ≤ 10
x1, x2 ≥ 0

# MAT 540 Week 5 Midterm Exam – Strayer University New

MAT 540 Midterm Exam Solution Week 5 LATEST

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MAT 540 Midterm Exam Solution – NEW

Chapter 1,11,12,14,15

Introduction to Management Science, (Taylor)

Chapter 1 Management Science

1) Management science involves the philosophy of approaching a problem in a subjective manner.

Diff: 1     Page Ref: 2

Section Heading: The Management Science Approach to Problem Solving

Keywords: scientific approach

AACSB: Analytic skills

2) Management science techniques can be applied only to business and military organizations.

Diff: 1     Page Ref: 2

Section Heading: The Management Science Approach to Problem Solving

Keywords: scientific approach, problem solving

AACSB: Analytic skills

3) Management scientists use the terms “data” and “information” interchangeably–that is, the two terms mean the same thing

Diff: 2     Page Ref: 4

Section Heading: The Management Science Approach to Problem Solving

Keywords: data

AACSB: Analytic skills

4) A management science solution can be either a recommended decision or information that helps a manager make a decision

Diff: 2     Page Ref: 5

Section Heading: The Management Science Approach to Problem Solving

Keywords: model, management science techniques

AACSB: Analytic skills

5) A variable is a value that is usually a coefficient of a parameter in an equation.

Diff: 1     Page Ref: 3

Section Heading: The Management Science Approach to Problem Solving

Keywords: variable

AACSB: Analytic skills

6) Parameters are known, constant values that are usually coefficients of variables in equations.

Diff: 1     Page Ref: 3

Section Heading: The Management Science Approach to Problem Solving

Keywords: parameter

AACSB: Analytic skills

7) Data are pieces of information from the problem environment.

Diff: 1     Page Ref: 4

Section Heading: The Management Science Approach to Problem Solving

Keywords: data

AACSB: Analytic skills

8) A model is a mathematical representation of a problem situation including variables, parameters, and equations.

Diff: 1     Page Ref: 3

Section Heading: The Management Science Approach to Problem Solving

Keywords: model, management science techniques

AACSB: Analytic skills

9) A management science technique usually applies to a specific model type.

Diff: 1     Page Ref: 3

Section Heading: The Management Science Approach to Problem Solving

Keywords: models, management science techniques

AACSB: Analytic skills

10) The first step of the management science process is to define the problem.

Diff: 2     Page Ref: 2

Section Heading: The Management Science Approach to Problem Solving

Keywords: management science process

AACSB: Analytic skills

11) Management science modeling techniques provide results that are known with certainty.

Diff: 2     Page Ref: 17

Section Heading: Management Science Modeling Techniques

Keywords: management science modeling techniques, certainty

AACSB: Analytic skills

12) The term “sensitivity analysis” refers to testing how a problem solution reacts to changes in one or more of the model parameters.

Diff: 1     Page Ref: 10

Section Heading: Model Building: Break-Even Analysis

Keywords: sensitivity analysis, parameter changes

13) Fixed costs depend on the number of items produced.

Diff: 1     Page Ref: 7

Section Heading: Model Building: Break-Even Analysis

Keywords: fixed cost, break-even analysis

AACSB: Analytic skills

14) Variable costs depend on the number of items produced.

Diff: 1     Page Ref: 7

Section Heading: Model Building: Break-Even Analysis

Keywords: variable cost, break-even analysis

15) Fixed cost is the difference between total cost and total variable cost.

Diff: 1     Page Ref: 8

Section Heading: Model Building: Break-Even Analysis

Keywords: total cost, break-even analysis

16) The break-even point is the volume that equates total revenue with total cost.

Diff: 1     Page Ref: 9

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

17) In general, an increase in price increases the break-even point if all costs are held constant.

Diff: 1     Page Ref: 10

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

18) If variable costs increase, but price and fixed costs are held constant, the break-even point will decrease.

Diff: 2     Page Ref: 11

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

19) Managers utilize spreadsheets to conduct their own analyses in management science studies.

Diff: 2     Page Ref: 12

AACSB: Analytic skills

20) Management science techniques focus primarily on observation, model construction, and implementation to find an appropriate solution to a problem.

Diff: 2     Page Ref: 15

Section Heading: Management Science Modeling Techniques

Keywords: mgt science modeling techniques, steps of the scientific method

AACSB: Analytic skills

21) Management science modeling techniques focus on model construction and problem solution.

Diff: 2     Page Ref: 15

Section Heading: Management Science Modeling Techniques

Keywords: mgt science model techniques, model constr, prob solution

AACSB: Analytic skills

22) A typical objective function might be written as 3S + 2R + 5Z ≤ 20.

Diff: 2     Page Ref: 4

Section Heading: The Management Science Approach to Problem Solving

Keywords: objective function

AACSB: Analytic skills

23) Decision Support Systems (DSS) use computers to help decision makers address complex problems.

Diff: 1     Page Ref: 20

Section Heading: Management Science Models in Decision Support Systems

Keywords: decision making, management science

24) In both an objective function and a constraint, the decision variables are represented by numbers.

Diff: 1     Page Ref: 4

Section Heading: The Management Science Approach to Problem Solving

Keywords: decision variables

AACSB: Analytic skills

25) Constraints usually appear as equations that are less than, equal to, or greater than a parameter.

Diff: 1     Page Ref: 4

Section Heading: The Management Science Approach to Problem Solving

Keywords: constraints

AACSB: Analytic skills

26) Enterprise Resource Planning (ERP) system is a data-oriented decision support system that utilizes specific management science solution procedures to solve individual problems such as cost-volume analysis.

Diff: 1     Page Ref: 21

Section Heading: Management Science Models in Decision Support Systems

Keywords: decision support systems

27) A key element of a decision support system (DSS) is the person using the system.

Diff: 2     Page Ref: 20

Section Heading: Management Science Models in Decision Support Systems

Keywords: decision support systems

AACSB: Analytic skills

28) Electronic data interchange (EDI) is a type of decision support system.

Diff: 1     Page Ref: 21

Section Heading: Management Science Models in Decision Support Systems

Keywords: decision support systems

AACSB: Analytic skills

29) A ________ is a symbol used to represent an item that can take on any value.

30) ________ are known, constant values that are coefficients of variables in equations.

31) ________ are pieces of information from the problem environment.

32) A ________ is a functional relationship including variables, parameters, and equations.

33) Management science techniques include ________ techniques, models that are represented as diagrams, presenting a pictorial representation of the system being analyzed.

34) An increase in output typically results in an increase in the ________ cost.

35) ________ techniques provide results that contain uncertainty, unlike mathematical programming techniques which are deterministic.

36) ________ costs are independent of the volume of goods produced and remain constant.

37) The difference between volume multiplied by price and the sum of fixed and variable costs is ________.

38) ________ depend on the number of items produced.

39) Total revenue minus total cost equals ________.

40) The ________ is the volume that equates total revenue with total cost.

41) A ________ represents a limitation to achieving maximum profits due to limited resources.

42) A ________ programming technique refers to a predetermined set of mathematical steps used to solve a problem.

43) One way to test how a management science model reacts to changes in its parameters is to conduct ________ analysis.

44) ________ consist of models that are represented as diagrams rather than as strictly mathematical techniques.

45) A management science technique that does not assume that all parameters are known with certainty is a(n) ________ technique.

46) A ________ is a computer-based system that helps decision-makers address complex problems that involve different parts of an organization and operations.

47) The relationship d = 5000 – 25p describes what happens to demand (d) as price (p) varies. Price can vary between \$10 and \$50. How many units can be sold when the price is \$10?

48) Researchers at John H. Stroger, Jr. Hospital of Cook County used ________ to address the problem of healthcare-associated infections in hospitals.

49) A production process requires a fixed cost of \$50,000. The variable cost per unit is \$25 and the revenue per unit is projected to be \$45. Write a mathematical expression for total cost.

50) A production process requires a fixed cost of \$50,000. The variable cost per unit is \$25 and the revenue per unit is projected to be \$45. Write a mathematical expression for total revenue.

51) A production process requires a fixed cost of \$50,000. The variable cost per unit is \$25 and the revenue per unit is projected to be \$45. Write a mathematical expression for total profit.

52) A production process requires a fixed cost of \$50,000. The variable cost per unit is \$25 and the revenue per unit is projected to be \$45. Find the break-even point.

53) A production process requires a fixed cost of \$50,000 and the variable cost per unit is \$25. The revenue per unit was projected to be \$45, but a recent marketing study shows that because of an emerging competitor, the revenue will be about 12% lower. How does this affect the break-even point?

54) Administrators at a university will charge students \$150 to attend a seminar. It costs \$3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs \$25 per student for the administrators to provide the course materials. How many students would have to register for the seminar for the university to break even?

55) Administrators at a university are planning to offer a summer seminar. It costs \$3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs \$25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even?

56) Administrators at a university are planning to offer a summer seminar. It costs \$3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs \$25 per student for the administrators to provide the course materials. If 30 students pay \$175 for the privilege of attending the seminar, how much of a profit (or loss) will be incurred?

57) A newly opened bed-and-breakfast projects the following:

Monthly fixed costs                                          \$8000

Variable cost per occupied room per night           \$40

Revenue per occupied room per night      \$165

Write the expression for total cost per month.

58) A newly opened bed-and-breakfast projects the following:

Monthly fixed costs                                        \$8000

Variable cost per occupied room per night           \$40

Revenue per occupied room per night      \$165

Write the expression for total revenue per month.

Diff: 2    Page Ref: 8

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

59) A newly opened bed-and-breakfast projects the following:

Monthly fixed costs                                        \$8000

Variable cost per occupied room per night           \$40

Revenue per occupied room per night      \$165

How many rooms would have to be occupied per month in order to break even?

60) A script writer has received an advance against royalties of \$10,000. The royalty rate is \$2 for every performance in the U.S., and \$3 for every performance outside the U.S. Define variables for this problem.

61) A business analyst describes his company’s profit function as 3x2 + 6x – 200. If x is the output volume, what statements can you make about the price, fixed cost, and variable cost?

62) A script writer has received an advance against royalties of \$10,000. The royalty rate is \$2 for every performance in the U.S., and \$3 for every performance outside the U.S. Write an expression that could be used to compute the number of performances in order to cover the advance.

63) Students are organizing a “Battle of the Bands” contest. They know that at least 100 people will attend. The rental fee for the hall is \$150 and the winning band will receive \$500. In order to guarantee that they break even, how much should they charge for each ticket?

64) A popular performer is scheduled to appear at a major city. The promoter is deciding between two venues, the larger of which costs \$20,000 to rent and the smaller of which costs \$12,000 to rent. Ticket prices for the smaller venue are \$20, but the promoter is unsure what to charge per ticket for the larger venue. If exactly 1000 customers arrive, what percentage change in ticket prices would make the profit at the large venue identical to that of the smaller venue?

65) A manufacturer buys peas for vegetable pies from two cooperatives. The price per unit is \$6 from cooperative A and \$5.50 per unit from cooperative B. Define variables that would tell how many units to purchase from each source.

66) A manufacturer buys peas for vegetable pies from two cooperatives. The price per unit is \$6 from cooperative A and \$5.50 per unit from cooperative B. Develop an objective function that would minimize the total cost.

67) A manufacturer buys peas for vegetable pies from two cooperatives. The price per unit is \$6 from cooperative A and \$5.50 per unit from cooperative B. The manufacturer needs at least 12,000 units of peas. Cooperative A can supply up to 8000 units, and cooperative B can supply at least 6000 units. Develop constraints for these conditions.

68) A group of professors struggles to craft a set of assessment questions for their operations management intro class. They want to cover four topic areas with at least four questions each and have no more than twenty questions total for the assessment. What would a set of constraints look like if they chose an optimization approach to the assessment?

69) What are some different types of decision support systems?

70) A manager of the cereal bar at the college campus has determined that the profit made for each bowl of Morning Buzz cereal sold, x, is equal to: Z = \$4x – 0.5x. Each bowl of Morning Buzz weighs 6 ounces, and the manager has 12 lbs (192 ounces) of cereal available each day, which can be written as the constraint, 6x ≤ 192. What maximum profit will be made from Morning Buzz if it is all sold in one day?

71) The College Coffee Café buys tea from three suppliers. The price per pound is \$15.00 from supplier A, \$17.50 from supplier B, and \$21.00 from supplier C. They have budgeted \$175 to purchase the tea. The café needs at least 12 pounds of tea, and supplier C can supply no more than 4 pounds. Develop constraints for these conditions.

72) The College Coffee Café receives a profit of \$1.25 for each cup of house tea that they sell, \$1.40 for each cup of the premium brand, and \$1.50 for each cup of their special blend. Develop an objective that maximizes profit.

73) The steps of the management science process are:

1. A) problem definition, model construction, observation, model solution, implementation.
2. B) observation, problem definition, model construction, model solution, implementation.
3. C) model construction, problem definition, observation, model solution, implementation.
4. D) observation, implementation, problem definition, model construction, model solution.

74) A model is a functional relationship that includes:

1. A) variables.
2. B) parameters.
3. C) equations.
4. D) all of the above

75) Which of the following is an equation or an inequality that expresses a resource restriction in a mathematical model?

1. A) a decision variable
2. B) an objective function
3. C) a constraint
4. D) a parameter

76) There is considerable overlap in the scientific method and management science techniques. Which of the following steps is shared between them?

1. A) observation
2. B) problem definition
3. C) model construction
4. D) implementation

77) Which of the following is incorrect with respect to the use of models in decision making?

1. A) They improve understanding of the problem.
2. B) They promote subjectivity in decision making.
3. C) They are generally easy to use.
4. D) They provide a systematic approach to problem solving.

Diff: 3     Page Ref: 3

Section Heading: The Management Science Approach to Problem Solving

Keywords: model, problem solving

AACSB: Analytic skills

78) The field of management science

1. A) approaches decision making irrationally with techniques based on the scientific method.
2. B) is another name for management or human resources management.
3. C) concentrates on the use of quantitative methods to assist managers in decision making.
4. D) is completely separate and distinct from all other disciplines.

Diff: 1     Page Ref: 2

Section Heading: The Management Science Approach to Problem Solving

Keywords: management science, operations research

AACSB: Analytic skills

79) The processes of problem observation

1. A) cannot be done until alternatives are proposed.
2. B) requires consideration of multiple criteria.
3. C) is the first step of decision making.
4. D) is the final step of problem solving.

Diff: 1     Page Ref: 2

Section Heading: The Management Science Approach to Problem Solving

Keywords: observation, problem observation, management science process

AACSB: Analytic skills

80) The limits of the problem and the degree to which it pervades other units in the organization must be included during the ________ step of the management science process.

1. A) observation
2. B) definition
3. C) solution
4. D) implementation

81) ________ involves determining the functional relationship between variables, parameters, and equations.

1. A) Problem observation
2. B) Problem definition
3. C) Model construction
4. D) Model solution

Diff: 1     Page Ref: 3

Section Heading: The Management Science Approach to Problem Solving

Keywords: management science process, model construction

AACSB: Analytic skills

82) Which steps of the management science process can either be a recommended decision or information that helps a manager make a decision?

1. A) model implementation
2. B) problem definition
3. C) model solution
4. D) problem formulation

Diff: 2     Page Ref: 3

Section Heading: The Management Science Approach to Problem Solving

Keywords: management science process, model solution

AACSB: Analytic skills

83) The quantitative analysis approach requires

1. A) mathematical expressions for the relationship.
2. B) uncomplicated problems.
3. C) the manager to have prior experience with similar problems.

Diff: 2     Page Ref: 3

Section Heading: The Management Science Approach to Problem Solving

Keywords: management science, operations research, quantitative analysis

AACSB: Analytic skills

84) The earliest developments and use of management science techniques was in the field of

1. A) military operations.
3. C) politics.
4. D) manufacturing.

Diff: 2     Page Ref: 5

Section Heading: The Management Science Approach to Problem Solving

Keywords: management science, operations research

AACSB: Analytic skills

85) The result of an effective decision making process should be monitored in order to

1. A) reveal the break-even point.
2. B) reveal errors in the implementation.
3. C) keep fixed and variable costs distinct.
4. D) change the scientific method.

Diff: 2     Page Ref: 7

Section Heading: The Management Science Approach to Problem Solving

Keywords: decision making process

AACSB: Analytic skills

86) The management science process does not include

1. A) feedback.
2. B) implementation.
3. C) subjective preference.
4. D) information.

Diff: 2     Page Ref: 2

Section Heading: The Management Science Approach to Problem Solving

Keywords: management science process

AACSB: Analytic skills

87) The indicator that results in total revenues being equal to total cost is called the

1. A) marginal cost.
2. B) marginal volume.
3. C) break-even point.
4. D) profit mix.

Diff: 1     Page Ref: 7

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

88) Variable cost

1. A) depends on the number of units produced.
2. B) plus marginal cost equals fixed cost.
3. C) is equal to total cost in deterministic models.
4. D) is the same as average cost.

Diff: 2     Page Ref: 7

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

89) The components of break-even analysis are

1. A) cost and profit.
2. B) volume and cost.
3. C) volume, cost and profit.
4. D) volume and profit.

Diff: 1     Page Ref: 7

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

90) ________ are generally independent of the volume of units produced and sold.

1. A) Fixed costs
2. B) Variable costs
3. C) Profits
4. D) Average cost

Diff: 1     Page Ref: 7

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

91) The purpose of break-even analysis is to determine the number of units of a product to sell that will

1. A) appeal to the consumer.
2. B) result in a profit.
3. C) result in a loss.
4. D) result in zero profit.

Diff: 2     Page Ref: 7

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

92) Variable cost does not include

1. A) raw materials and resources.
2. B) staff and management salaries.
3. C) material handling and freight.
4. D) direct labor and packaging.

Diff: 2     Page Ref: 7

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

93) Which variable is not a component of break-even analysis?

1. A) fixed costs
2. B) variable costs
3. C) number of employees
4. D) number of customers

Diff: 1     Page Ref: 7

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

94) At the break-even point,

1. A) total revenue equals total cost.
2. B) profit is maximized.
3. C) revenue is maximized.
4. D) costs are minimized.

Diff: 1     Page Ref: 9

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

95) If the price increases, but fixed and variable costs do not change, the break-even point

1. A) decreases.
2. B) increases.
3. C) remains the same.
4. D) may increase or decrease, depending on sales.

Diff: 2     Page Ref: 10

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

96) If the price decreases, but fixed and variable costs do not change, the break-even point

1. A) decreases
2. B) increases
3. C) remains the same
4. D) may increase or decrease, depending on sales

Diff: 2     Page Ref: 10

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

97) The term ________ refers to testing how a problem solution reacts to changes in one or more of the model parameters.

1. A) graphical solution
2. B) decision analysis
3. C) sensitivity analysis
4. D) break-even analysis

Diff: 2     Page Ref: 10

Section Heading: Model Building: Break-Even Analysis

Keywords: sensitivity analysis, modeling process

AACSB: Analytic skills

98) If fixed costs decrease, but variable cost and price remain the same, the break-even point

1. A) decreases.
2. B) increases.
3. C) remains the same.
4. D) may increase or decrease depending on sales.

Diff: 2     Page Ref: 12

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

99) If fixed costs increase, but variable cost and price remain the same, the break-even point

1. A) decreases.
2. B) increases.
3. C) remains the same.
4. D) may increase or decrease depending on sales.

Diff: 2     Page Ref: 12

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

100) EKA manufacturing company produces part #2206 for the aerospace industry. Each unit of part #2206 is sold for \$15. The unit production cost of part #2206 is \$3. The fixed monthly cost of operating the production facility is \$3000. How many units of part #2206 have to be sold in a month to break even?

1. A) 166.67
2. B) 200
3. C) 250
4. D) 500

Diff: 2     Page Ref: 9

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

101) EKA manufacturing company produces part #2206 for the aerospace industry. The unit production cost of part #2206 is \$3. The fixed monthly cost of operating the production facility is \$3000. Next month’s demand for part #2206 is 200 units. How much should the company charge for each unit of part #2206 to break even?

1. A) \$12
2. B) \$15
3. C) \$18
4. D) \$20

Diff: 2     Page Ref: 9

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

102) A bed-and-breakfast breaks even every month if they book 30 rooms over the course of a month. Their fixed cost is \$6000 per month and the revenue they receive from each booked room is \$180. What is their variable cost per occupied room?

1. A) \$130
2. B) \$140
3. C) \$148
4. D) \$160

Diff: 3     Page Ref: 9

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

103) Administrators at a university will charge students \$150 to attend a seminar. It costs \$3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs \$25 per student for the administrators to provide the course materials. How many students would have to register for the seminar for the university to break even?

1. A) 18
2. B) 20
3. C) 24
4. D) 30

Diff: 2     Page Ref: 9

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

104) A university is planning a seminar. It costs \$3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs \$25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even?

1. A) \$120
2. B) \$150
3. C) \$175
4. D) \$200

Diff: 2    Page Ref: 9

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

105) It costs \$50,000 to start a production process. Variable cost is \$25 per unit and revenue is \$45 per unit. What is the break-even point?

1. A) 1000 units
2. B) 1111 units
3. C) 2000 units
4. D) 2500 units

Diff: 1     Page Ref: 9

Section Heading: Model Building: Break-Even Analysis

Keywords: break-even analysis

AACSB: Analytic skills

106) Which of the following statements is false?

1. A) Decision models selectively describe the managerial situation.
2. B) Decision models consider all factors from the real world.
3. C) Decision models designate performance measures that reflect objectives.
4. D) Decision models designate decision variables.

Diff: 2     Page Ref: 3

Section Heading: The Management Science Approach to Problem Solving

Keywords: models, decision models, modeling techniques

AACSB: Analytic skills

107) Decision support systems and sensitivity analysis are useful management science tools for answering the question:

1. A) by when?
2. B) who else?
3. C) how much?
4. D) what if?

Diff: 2     Page Ref: 21

Section Heading: Management Science Models in Decision Support Systems

Keywords: decision support systems

AACSB: Analytic skills

108) A difficult aspect of using spreadsheets to solve management science problems is

1. A) obtaining the solution to standard management science problems.
2. B) data entry.
3. C) performing sensitivity analysis.
4. D) setting up a spreadsheet with complex models and formulas.

Diff: 2     Page Ref: 12

AACSB: Analytic skills

109) A technique that assumes certainty in its solution is referred to as

1. A) stochastic.
2. B) probabilistic.
3. C) deterministic.
4. D) parametric.

Diff: 2     Page Ref: 17

Section Heading: Management Science Modeling Techniques

Keywords: modeling, models, modeling techniques

AACSB: Analytic skills

110) Classification of management science techniques does not recognize

1. A) linear mathematical programming.
2. B) probabilistic techniques.
3. C) network techniques.
4. D) computer programming.

Diff: 1     Page Ref: 16

Section Heading: Management Science Modeling Techniques

Keywords: management science techniques, classification of techniques

AACSB: Analytic skills

111) Linear mathematical programming techniques assume that all parameters in the models are

1. A) known with certainty.
2. B) unknown.
3. C) predictable.
4. D) unpredictable.

Diff: 2     Page Ref: 16

Section Heading: Management Science Modeling Techniques

Keywords: management science techniques

AACSB: Analytic skills

112) Decision analysis is a ________ technique.

1. A) linear mathematical programming
2. B) probabilistic
3. C) network
4. D) non-linear programming technique

Diff: 1     Page Ref: 17

Section Heading: Management Science Modeling Techniques

Keywords: management science techniques

AACSB: Analytic skills

113) Which one of the following techniques is not a mathematical programming technique?

1. A) linear programming models
2. B) transportation models
3. C) analytical hierarchy process
4. D) integer linear programming technique

Diff: 2     Page Ref: 17

Section Heading: Management Science Modeling Techniques

Keywords: management science techniques

AACSB: Analytic skills

114) Which one of the following management science methods is not a probabilistic technique?

1. A) assignment models
2. B) decision analysis
3. C) queuing analysis
4. D) statistical analysis

Diff: 2     Page Ref: 17

Section Heading: Management Science Modeling Techniques

Keywords: management science techniques

AACSB: Analytic skills

115) A baker uses organic flour from a local farmer in all of his baked goods. For each batch of bread (x1), he uses 4 pounds of flour. For a batch of cookies (x2), he uses 3 pounds, and for a batch of muffins (x3) he uses 2 pounds. The local farmer can supply him with no more than 24 pounds per week. The constraint that represents this condition is:

1. A) x1 ≤ 8, x2 ≤ 8, x3 ≤ 8
2. B) x1 + x2 + x3 ≥ 24
3. C) x1 + x2 + x3 ≤ 24
4. D) 4x1 + 3x2 + 2x3 ≤ 24

Diff: 3     Page Ref: 16

Section Heading: Management Science Modeling Techniques

Keywords: constraints

AACSB: Analytic skills

116) An objective function

1. A) shows where the break-even point is.
2. B) describes how much of a resource can be used.
3. C) can represent costs or profits.
4. D) describes something to be maximized.

Diff: 2     Page Ref: 16

Section Heading: Management Science Modeling Techniques

Keywords: objective function, model construction

AACSB: Analytic skills

117) Larry’s Fish Market buys salmon (S) for \$5 per pound and a local whitefish (W) for \$3.50 per pound. Larry wants to minimize his cost, but he cannot spend more than \$160. The objective function that minimizes these costs for Larry is:

1. A) 5S + 3.5W ≤ 160
2. B) Min 5S + 3.5 W
3. C) Max 5S + 3.5 W
4. D) Min 5S + 3.5W ≥ 160

Diff: 3     Page Ref: 4

Section Heading: Management Science Modeling Techniques

Keywords: objective function, model construction

AACSB: Analytic skills

118) It’s time to buy pet food again and Lisa heads to the grocery store with \$40 in her purse, leaving her seven hungry cats and four hungry dogs at home. Dog food costs \$1 per can and cat food costs \$0.50 per can. Dogs eat two full cans of food each day but cats eat only one can. Lisa would like to buy enough food to last through her three-day weekend. What is an appropriate objective function for this scenario?

1. A) Min Z = 1D + 0.5C
2. B) Min Z = 2D + 1C
3. C) Min Z = D + C ≤ 40
4. D) Min Z = D + C ≥ 3

Diff: 3     Page Ref: 4

Section Heading: The Management Science Approach to Problem Solving

Keywords: objective function

AACSB: Analytic skills

119) It’s time to buy pet food again and Lisa heads to the grocery store with \$40 in her purse, leaving her seven hungry cats and four hungry dogs at home. Dog food costs \$1 per can and cat food costs \$0.50 per can. Dogs eat two full cans of food each day but cats eat only one can. Lisa would like to buy enough food to last through her three-day weekend. What is one appropriate constraint for this scenario?

1. A) 7C + 4D ≥ 3
2. B) 1C + 2D ≤ 40
3. C) .5C + 1D ≤ 40
4. D) 7C + 4D ≥ 1.5

Diff: 3     Page Ref: 4

Section Heading: The Management Science Approach to Problem Solving

Keywords: constraints

AACSB: Analytic skills

120) Marriott used which of the following management science techniques to help improve profit by \$120 million over two years?

1. A) optimization, decision analysis, and forecasting
2. B) forecasting, queuing theory, and inventory analysis
3. C) queuing theory, optimization, and inventory analysis
4. D) forecasting, simulation, and optimization

Diff: 3     Page Ref: 6

Section Heading: Management Science Modeling Techniques

Keywords: management science, management scientist

AACSB: Analytic skills

121) Which of these decision support systems is the most comprehensive with respect to an entire organization?

2. B) an ERP
3. C) QM for Windows
4. D) OLAP

Diff: 2     Page Ref: 20

Section Heading: Management Science Models in Decision Support Systems

Keywords: decision support systems

AACSB: Analytic skills

Introduction to Management Science, (Taylor)

Chapter 11 Probability and Statistics

1) Deterministic techniques assume that no uncertainty exists in model parameters.

Diff: 1   Page Ref: 503

Keywords: deterministic techniques

2) Probabilistic techniques assume that no uncertainty exists in model parameters.

Diff: 1   Page Ref: 503

Keywords: probabilistic techniques

3) Objective probabilities that can be stated prior to the occurrence of an event are classical or a priori.

Diff: 2   Page Ref: 503

Keywords: objective probabilities, classical probabilities

4) Objective probabilities that are stated after the outcomes of an event have been observed are relative frequencies.

Diff: 2   Page Ref: 503

Keywords: relative frequencies

5) Relative frequency is the more widely used definition of objective probability.

Diff: 1   Page Ref: 504

Keywords: relative frequencies

6) Subjective probability is an estimate based on personal belief, experience, or knowledge of a situation.

Diff: 2   Page Ref: 504

Keywords: subjective probability

7) An experiment is an activity that results in one of several possible outcomes.

Diff: 1   Page Ref: 505

Keywords: experiment

8) The events in an experiment are mutually exclusive if only one can occur at a time.

Diff: 1   Page Ref: 505

Keywords: mutually exclusive events

9) In a given experiment, the probabilities of all mutually exclusive events sum to one.

Diff: 1   Page Ref: 505

Keywords: mutually exclusive events, rules of probability

10) A set of events is collectively exhaustive when it includes all the events that can occur in an experiment.

Diff: 2   Page Ref: 506

Keywords: collectively exhaustive events

11) A marginal probability is the probability of a single event occurring.

Diff: 1   Page Ref: 506

Keywords: marginal probability

12) A Venn diagram visually displays mutually exclusive and non-mutually exclusive events.

Diff: 2   Page Ref: 506

Keywords: Venn diagram

13) A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously.

Diff: 2   Page Ref: 506

Keywords: joint probability

14) A conditional probability is the probability that an event occurs given that another event has already occurred.

Diff: 1   Page Ref: 508

Section Heading: Statistical Independence and Dependence

Keywords: conditional probability

15) Conditional probabilities are shown in Venn diagrams.

Diff: 1   Page Ref: 506

Keywords: conditional probability

16) Probability trees are used only to compute conditional probabilities.

Diff: 2   Page Ref: 509

Section Heading: Statistical Independence and Dependence

Keywords: probability tree, conditional probability

17) A succession of events that does not affect other events is independent.

Diff: 1   Page Ref: 508

Section Heading: Statistical Independence and Dependence

Keywords: independence

18) A binomial probability distribution indicates the probability of r successes in n trials.

Diff: 2   Page Ref: 510

Section Heading: Statistical Independence and Dependence

Keywords: binomial probability distribution

AACSB: Analytic skills

19) A continuous random variable may assume only integer values within a given interval.

Diff: 1   Page Ref: 517

Keywords: continuous random variables

AACSB: Analytic skills

20) Seventy-two percent of all observations fall within one standard deviation of the mean if the data is normally distributed.

Diff: 1   Page Ref: 519

Keywords: normal distribution

AACSB: Analytic skills

21) Another name for the mean of a probability distribution is its expected value.

Diff: 1   Page Ref: 516

Keywords: expected value

AACSB: Analytic skills

22) The expected value of a discrete random variable is greater than or equal to zero.

Diff: 1   Page Ref: 516

Keywords: expected value

23) The variance of a discrete random variable is always greater than or equal to zero.

Diff: 1   Page Ref: 516

Keywords: expected value

24) The expected value of a random variable is computed by multiplying the sum of each possible value of the variable by the probability of that random variable.

Diff: 1   Page Ref: 516

Keywords: expected value

AACSB: Analytic skills

25) The variance of a random variable is computed by multiplying each possible value of the variable by its probability and summing these products.

Diff: 1   Page Ref: 516

Keywords: variance

AACSB: Analytic skills

26) For a typical normally distributed random variable, the standard deviation is equal to the variance.

Diff: 1   Page Ref: 518

Keywords: normal distribution

27) A normally distributed random variable has a mean of zero and a standard deviation of one.

Diff: 1   Page Ref: 517-518

Keywords: normal distribution

28) The standard normal distribution has a mean of one and a standard deviation of zero.

Diff: 1   Page Ref: 519

Keywords: standard normal distribution

29) The area under the normal curve represents probability.

Diff: 1   Page Ref: 518

Keywords: norm distrib, probability calculations with normal distribution

30) There is just as great a chance of a normally distributed random variable being over one standard deviation above the mean as there is being one standard deviation below the mean.

Diff: 1   Page Ref: 518

Keywords: norm distrib, probability calculations with normal distribution

AACSB: Analytic skills

31) An inspector correctly identifies defective products 90% of the time. For the next 10 products, the probability that he makes fewer than two incorrect inspections is 0.736.

Diff: 2   Page Ref: 510

Section Heading: Statistical Independence and Dependence

Keywords: binomial distribution

AACSB: Analytic skills

32) In Bayesian analysis, additional information is used to alter the conditional probability of the occurence of an event.

Diff: 1   Page Ref: 514

Section Heading: Statistical Independence and Dependence

Keywords: conditional probability

33) Objective probabilities that can be stated prior to the occurrence of an event are ________.

Diff: 1   Page Ref: 503

Keywords: probabilistic techniques, objective/classical probabilities

34) ________ probability is an estimate based on a personal belief, experience, and knowledge of a situation.

35) The events in an experiment are ________ if only one can occur at a time.

36) The term for including all possible events that can occur in an experiment is ________.

37) The cumulative probability for all six outcomes of tossing a fair die should end with the value ________.

38) The fact that the first toss of a coin has no effect on the outcome of the second toss of the coin suggests that these events are ________.

39) The collectively exhaustive set of events for flipping a coin is ________.

40) A ________ organizes numerical data to describe the events of an experiment.

41) A Venn diagram depicting two circles that do not overlap or touch in any way represents events that are ________.

42) A ________ is the probability of occurence of a single event.

43) ________ can enable one to improve marginal probabilities of the occurrence of an event by gathering additional information.

44) A succession of events that do not affect each other are ________.

45) A ________ probability is the probability that an event will occur given that another event has already occurred.

46) In a binomial distribution process, there are ________ possible outcomes.

47) One of the properties of the ________ distribution is that the probability of success remains constant over time.

48) Altered marginal probability of an event based on additional information is a ________ probability.

49) The ________ of a random variable is computed by multiplying each possible value of the variable by its probability and summing these products.

50) If events A and B are independent, then P(AB) = ________.

51) If events A and B are independent, then P(A|B) = ________.

52) If two events A and B are not mutually exclusive, then P(A or B) = ________.

53) ________ is a measure of dispersion of random variable values about the expected value.

54) A continuous random variable can take on a(n) ________ number of values within a given interval.

55) The ________ test is a statistical test to see if an observed data fit a particular probability distribution.

56) The ________ normal distribution has a mean of 0 and a standard deviation of 1.

57) Almost all of the data from a normal distribution fall within ________ standard deviations of the mean.

58) The expected value of the standard normal distribution is equal to ________.

59) The standard deviation of the standard normal distribution is equal to ________.

Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y.

60) What is the probability that Jim will be accepted at both universities?

61) What is the probability that Jim will not be accepted at either university?

62) What is the probability that Jim will be accepted by at least one of the two universities?

Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category.

Male (M) Female (F)

Job

Salaried staff (SS)              30             50

Hourly staff (HS)             60             40

63) If an employee is selected at random, what is the probability that the employee is male?

64) If an employee is selected at random, what is the probability that the employee is male and salaried staff?

65) If an employee is selected at random, what is the probability that the employee is female given that the employee is a salaried staff member?

66) If an employee is selected at random, what is the probability that the employee is female or works as a member of the administration

The Dean’s Office keeps tracks of student complaints received each week. The probability distribution for complaints can be represented as a table as shown below. The random variable xi represents the number of complaints, and p(xi) is the probability of receiving xi complaints.

 0 1 2 3 4 5 6 p() 0.1 0.15 0.18 0.2 0.2 0.1 .07

67) What is the probability that they receive less than 3 complaints in a week?

68) What is the average number of complaints received per week?

69) A fair die is rolled nine times. What is the probability that an odd number (1, 3, or 5) will occur less than 3 times?

70) A fair die is rolled 8 times. What is the probability that an even number (2, 4, or 6) will occur between 2 and 4 times?

A company markets educational software products, and is ready to place three new products on the market. Past experience has shown that for this particular software, the chance of “success” is 80%. Assume that the probability of success is independent for each product.

71) Find the probability that exactly 1 of the 3 products is successful.

72) Find the probability that none of the 3 products is successful.

73) If X has the following probability distribution

X        1     2     3      4

P(X)   .1    .5    .2     .2

Compute the expected value of X.

74) Assume X has the following probability distribution :

X         1       2       3       4

P(X)    .1      .5      .2      .2

Compute the standard deviation of X.

75) If x is normally distributed with a mean of 10 and a standard deviation of 3, then P(x ≤ 6) is equal to P( Z ≤ _____)?

76) For a standard normal distribution, what is the probability that z is greater than 1.75?

Two psychology majors, in two different sections of Clinical Psychology, were comparing test scores. The following gives the students’ scores, class mean, and standard deviation for each section:

Section 1      Section 2

Student score                   84                 75

Mean                                 75                 60

Standard deviation            7                   8

77) What is the z-score of the student from section 1 and what is the probability that a student in section 1 will score higher than 84?

78) What is the z-score of the student from section 2 and what is the probability that a student in section 2 will score higher than 75?

79) Which student scored better compared to the rest of their section?

80) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is larger than 21 oz?

81) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf of bread is larger than 23 oz?

82) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is less than 24 oz?

83) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is between 20.75 and 23.25 oz?

84) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is between 21.75 and 22.25 oz?

85) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is more than 24 oz?

86) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is more than 22.25 oz?

87) A life insurance company wants to estimate its annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the plan recipients would receive payments beyond age 75?

88) A life insurance company wants to estimate its annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the participants die before they reach the age of 65?

89) A life insurance company wants to estimate its annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. By what age have 80% of the plan participants passed away?

90) For the normal distribution, the mean plus and minus 1.96 standard deviations will include what percent of the observations?

91) What is the area under the normal curve for Z ≥ 1.79?

92) A study of a company’s practice regarding the payment of invoices revealed that on the average an invoice was paid 20 days after it was received. The standard deviation equaled 5 days. Assuming that the distribution is normal, what percent of the invoices is paid within 15 days of receipt?

93) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. Assuming the weights of the crabs are normally distributed, what is the probability that a randomly selected crab will weigh more than 2.2 pounds?

94) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. Assuming the weights of crabs are normally distributed, what is the probability that a randomly selected crab will weigh between 1 and 2 pounds?

95) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. Assuming the weights of crabs are normally distributed, the probability that a randomly selected crab will weigh less than 1.2 pounds is ________.

96) A research scientist has observed the monkeys of the Nandi Hills outside of Bangalore for the last twenty years, carefully cataloging their preferences for a number of food items. An unsuspecting tourist leaves his can of soda unattended. Describe the type of probability the research scientist can assign to the likelihood that the soda will become the monkey’s next meal. Then contrast this type of probability with the other of the two basic types.

97) What are the differences between deterministic and probabilistic techniques?

Horatio Oscar Vineeth Lane (HOV Lane for short) records his commute times for a period of one month and assigned them to five different categories as shown in the table.

 Commute Length Number of Observations commute time <10 minutes 1 10 ≤ commute time < 20 minutes 2 20 ≤ commute time < 30 minutes 4 30 ≤ commute time < 40 minutes 9 40 ≤ commute time < 50 minutes 4

98) What is the likelihood that the commute will take 30 minutes or longer?

Diff: 1   Page Ref: 508

Keywords: cumulative probability distribution

AACSB: Analytic skills

99) What is the cumulative probability for the three shortest commute categories?

100) What is the average commute time for HOV Lane?

101) Assume that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2. Find the probability that X is between 48 and 55.

102) A paint manufacturer’s production process is normally distributed with a mean of 100,000 gallons and a standard deviation of 10,000 gallons. Management wants to create an incentive bonus for the production crew when the daily production exceeds the 94th percentile of the distribution. At what level of production should management pay the incentive bonus?

An online sweepstakes has the following payoffs and probabilities. Each person is limited to one entry.

103) The probability that someone wins any money is ________.

104) The probability of winning at least \$1000 is ________.

105) ________ techniques assume that no uncertainty exists in model parameters.

1. A) Probability
2. B) Probabilistic
3. C) Deterministic
4. D) Distribution

106) ________ probability is an estimate based on personal belief, experience, or knowledge of a situation.

1. A) Binomial
2. B) Subjective
3. C) Marginal
4. D) Joint

Diff: 2   Page Ref: 504

Keywords: subjective probability

107) Objective probabilities that can be stated prior to the occurrence of an event are

1. A) deterministic or probabilistic.
2. B) subjective or objective.
3. C) classical or a priori.
4. D) relative or subjective.

Diff: 2   Page Ref: 503

Keywords: classical (or a priori) probability

108) The events in an experiment are ________ if only one can occur at a time.

1. A) mutually exclusive
2. B) non-mutually exclusive
3. C) mutually inclusive
4. D) independent

Diff: 1   Page Ref: 505

Keywords: mutually exclusive events

109) In a given experiment the probabilities of mutually exclusive events sum to:

1. A) 0
2. B) 0.5
3. C) 1
4. D) This cannot be answered without knowing the probability values of the events.

Diff: 1   Page Ref: 505

Keywords: mutually exclusive events

110) A ________ probability is the probability of a single event occurring.

1. A) subjective
2. B) binomial
3. C) marginal
4. D) joint

Diff: 1   Page Ref: 506

Keywords: marginal probability

111) A frequency distribution is an organization of ________ data about the events in an experiment.

1. A) quantitative
2. B) integer
3. C) qualitative
4. D) unknown

Diff: 1   Page Ref: 505

Keywords: frequency distribution

112) Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. What is the probability that Jim will be accepted at both universities?

1. A) .65
2. B) .25
3. C) .20
4. D) .09

Diff: 2   Page Ref: 505

Keywords: multiplication of probabilities

AACSB: Analytic skills

113) Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. What is the probability that Jim will not be accepted at either university?

1. A) .30
2. B) .36
3. C) .44
4. D) .56

Diff: 2   Page Ref: 506

Keywords: multiplication of probabilities

AACSB: Analytic skills

114) Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category.

Male (M) Female (F)

Job

Salaried staff (SS)              30             50

Hourly staff (HS)             60             40

If an employee is selected at random, what is the probability that the employee is female or works as a member of the administration?

1. A) .17
2. B) .67
3. C) .70
4. D) .73

Diff: 2   Page Ref: 508

Keywords: not mutually exclusive events, addition rule

AACSB: Analytic skills

115) A ________ probability distribution indicates the probability of r successes in n trials.

1. A) joint
2. B) subjective
3. C) marginal
4. D) binomial

Diff: 2   Page Ref: 510

Section Heading: Statistical Independence and Dependence

Keywords: binomial probability distribution

116) The probability of independent events occurring in succession is computed by ________ the probabilities of each event.

1. A) multiplying
3. C) subtracting
4. D) dividing

Diff: 2   Page Ref: 508

Section Heading: Statistical Independence and Dependence

Keywords: independent events

117) A ________ probability is the probability that an event will occur given that another event has already occurred.

1. A) subjective
2. B) objective
3. C) conditional
4. D) binomial

Diff: 2   Page Ref: 508

Section Heading: Statistical Independence and Dependence

Keywords: conditional probability

118) In Bayesian analysis, additional information is used to alter the ________ probability of the occurrence of an event.

1. A) marginal
2. B) conditional
3. C) binomial
4. D) revised

Diff: 2   Page Ref: 514

Section Heading: Statistical Independence and Dependence

Keywords: marginal probability

119) Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category.

Male (M) Female (F)

Job

Salaried staff (SS)              30             50

Hourly staff (HS)             60             40

If an employee is selected at random, what is the probability that the employee is female given that the employee is a salaried staff member?

1. A) .50
2. B) .60
3. C) .625
4. D) .70

Diff: 2   Page Ref: 510

Section Heading: Statistical Independence and Dependence

Keywords: conditional probability

AACSB: Analytic skills

120) A ________ probability is the altered marginal probability of an event based on additional information.

1. A) posterior
2. B) joint
3. C) marginal
4. D) conditional

Diff: 2   Page Ref: 514

Section Heading: Statistical Independence and Dependence

Keywords: posterior (revised) probability

121) Mutually exclusive events are

1. A) events with identical probabilities.
2. B) events that have no outcomes in common.
3. C) events that have no effect on each other.
4. D) events that are represented in a Venn diagram by two overlapping circles.

Diff: 2   Page Ref: 505

Keywords: mutually exclusive events

122) Bayesian analysis involves a(n) ________ probability.

1. A) a priori
2. B) posterior
3. C) joint
4. D) relative frequency

Diff: 2   Page Ref: 514

Section Heading: Statistical Independence and Dependence

Keywords: Bayesian analysis

123) In a ________ distribution, for each of n trials, the event always has the same probability of occurring.

1. A) binomial
2. B) joint
3. C) frequency
4. D) standard

Diff: 2   Page Ref: 510

Section Heading: Statistical Independence and Dependence

Keywords: binomial distribution

124) Experiments with repeated independent trials will be described by the binomial distribution if

1. A) each trial result influences the next.
2. B) each trial has exactly two outcomes whose probabilities do not change.
3. C) the trials are continuous.
4. D) the time between trials is constant.

Diff: 2   Page Ref: 510

Section Heading: Statistical Independence and Dependence

Keywords: binomial distribution

125) In a binomial distribution, for each of n trials, the event

1. A) time between trials is constant.
2. B) always has the same probability of occurring.
3. C) result of the first trial influence the next trial.
4. D) trials are continuous.

Diff: 2   Page Ref: 510

Section Heading: Statistical Independence and Dependence

Keywords: binomial distribution

126) A fair die is rolled nine times. What is the probability that an odd number (1, 3, or 5) will occur less than 3 times?

1. A) .0899
2. B) .2544
3. C) .7456
4. D) .9101

Diff: 2   Page Ref: 510

Section Heading: Statistical Independence and Dependence

Keywords: binomial distribution

AACSB: Analytic skills

127) A fair die is rolled 8 times. What is the probability that an even number (2, 4, or 6) will occur between 2 and 4 times?

1. A) .2188
2. B) .4922
3. C) .6016
4. D) .8204

Diff: 2   Page Ref: 510

Section Heading: Statistical Independence and Dependence

Keywords: binomial distribution

AACSB: Analytic skills

128) A company markets educational software products and is ready to place three new products on the market. Past experience has shown that for this particular software, the chance of “success” is 80%. Assume that the probability of success is independent for each product. What is the probability that exactly 1 of the 3 products is successful?

1. A) 0.80
2. B) 0.032
3. C) 0.24
4. D) 0.096

Diff: 2   Page Ref: 510

Section Heading: Statistical Independence and Dependence

Keywords: binomial distribution

AACSB: Analytic skills

129) ________ is a measure of the dispersion of random variable values about the expected value or mean.

1. A) Standard deviation
2. B) Sample mean
3. C) Population mean
4. D) Expected value

Diff: 2   Page Ref: 515

Keywords: variance, standard deviation

130) An automotive center keeps tracks of customer complaints received each week. The probability distribution for complaints can be represented as the table shown below. The random variable xi represents the number of complaints, and p(xi) is the probability of receiving xi complaints.

 0 1 2 3 4 5 6 p() 0.1 0.15 0.18 0.2 0.2 0.1 .07

What is the average number of complaints received per week?

1. A) 2.12
2. B) 3.32
3. C) 4.12
4. D) 2.83

Diff: 2   Page Ref: 516

Keywords: expected value

AACSB: Analytic skills

131) The expected value of the standard normal distribution is equal to:

1. A) 0
2. B) 1
3. C) 1.5
4. D) 2

Diff: 1   Page Ref: 519

Keywords: expected value

132) The area under the normal curve represents probability, and the total area under the curve sums to:

1. A) 0
2. B) 0.5
3. C) 1
4. D) 2

Diff: 2   Page Ref: 517

Keywords: normal distribution

133) The ________ and variance are derived from a subset of the population data and are used to make inferences about the population.

1. A) population variance
2. B) population standard deviation
3. C) population mean
4. D) sample mean

Diff: 1   Page Ref: 511

Keywords: mean and variance

134) Under the normal curve, the area between z = 1 and z = -2 includes approximately ________ of the values.

1. A) 98%
2. B) 95%
3. C) 85%
4. D) 82%

Diff: 3   Page Ref: 520

Keywords: normal distribution

AACSB: Analytic skills

135) For the normal distribution, the mean plus and minus 1.96 standard deviations will include what percent of the observations?

1. A) 84%
2. B) 90%
3. C) 95%
4. D) 97%

Diff: 1   Page Ref: 520

Keywords: normal distribution

AACSB: Analytic skills

136) The weight of a jar of jelly is normally distributed with a mean of 16 oz and a standard deviation of 0.02 oz. What is the probability that a jar of jelly contains less than 16 oz?

1. A) .1915
2. B) .3085
3. C) .5000
4. D) .7257

Diff: 2   Page Ref: 520

Keywords: norm distrib, probability calculations with normal distribution

AACSB: Analytic skills

137) The weight of a jar of jelly is normally distributed with a mean of 16 oz and a standard deviation of 0.02 oz. What is the probability that a jar of jelly contains more than 16.03 oz?

1. A) .0668
2. B) .1587
3. C) .4332
4. D) .9332

Diff: 2   Page Ref: 519

Keywords: norm distrib, probability calculations with normal distribution

AACSB: Analytic skills

138) Under the normal curve, the area between z = 2 and z = -2 includes ________ of the values.

1. A) 98%
2. B) 96%
3. C) 95%
4. D) 93%

Diff: 2   Page Ref: 519

Keywords: normal distribution

AACSB: Analytic skills

139) The metropolitan airport commission is considering the establishment of limitations on noise pollution around a local airport. At the present time, the noise level per jet takeoff in one neighborhood near the airport is approximately normally distributed with a mean of 100 decibels and a standard deviation of 3 decibels. What is the probability that a randomly selected jet will generate a noise level of more than 105 decibels?

1. A) 0.0228
2. B) 0.0475
3. C) 0.0485
4. D) 0.0500

Diff: 2   Page Ref: 520

Keywords: normal distribution

AACSB: Analytic skills

140) For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.2910. The value of Z is:

1. A) 0.17
2. B) 0.81
3. C) 1.25
4. D) 1.65

Diff: 2   Page Ref: 520

Keywords: normal distribution

AACSB: Analytic skills

141) For some value of Z, the probability that a standard normal variable is below Z is 0.3783. The value of Z is:

1. A) -0.81
2. B) -0.31
3. C) 0.82
4. D) 1.55

Diff: 2   Page Ref: 519

Keywords: standard normal distribution

AACSB: Analytic skills

142) For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3554. The value of Z is:

1. A) 0.31
2. B) 0.36
3. C) 0.95
4. D) 1.06

Diff: 2   Page Ref: 519

Keywords: norm distrib, probability calculations with normal distribution

AACSB: Analytic skills

143) If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.

1. A) 0.3551
2. B) 0.3085
3. C) 0.2674
4. D) 0.1915

Diff: 1   Page Ref: 520

Keywords: normal distribution

AACSB: Analytic skills

144) Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. Find the probability that a randomly selected college student will take between 2 and 6 minutes to find a parking spot in the main parking lot.

1. A) 0.1950
2. B) 0.4772
3. C) 0.4332
4. D) 0.6247

Diff: 1   Page Ref: 520

Keywords: norm distrib, probability calculations with normal distribution

AACSB: Analytic skills

145) Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. What time is exceeded by approximately 75% of the college students when trying to find a parking spot in the main parking lot?

1. A) 3.65 minutes
2. B) 5.75 minutes
3. C) 6.36 minutes
4. D) 9.21 minutes

Diff: 2   Page Ref: 519

Keywords: normal distribution

AACSB: Analytic skills

146) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. What weight is exceeded by 2% of all of the crabs? (Assume the weights are normally distributed.)

1. A) 0.78 pounds
2. B) 1.82 pounds
3. C) 2.42 pounds
4. D) 4.36 pounds

Diff: 2   Page Ref: 520

Keywords: norm distrib, probability calculations with normal distribution

AACSB: Analytic skills

147) A professor would like to assign grades such that 5% of students receive As. If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an A? (Round your answer.)

1. A) 80
2. B) 83
3. C) 90
4. D) 93

Diff: 2   Page Ref: 520

Keywords: norm distrib, probability calculations with normal distribution

AACSB: Analytic skills

148) A professor would like to assign grades such that 7% of students receive Fs. If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an F? (Round your answer.)

1. A) 43
2. B) 49
3. C) 50
4. D) 55

Horatio Oscar Vineeth Lane (HOV Lane for short) records his commute times for a period of one month and assigned them to five different categories as shown in the table.

 Commute Length Number of Observations commute time <10 minutes 1 10 ≤ commute time < 20 minutes 2 20 ≤ commute time < 30 minutes 4 30 ≤ commute time < 40 minutes 9 40 ≤ commute time < 50 minutes 4

149) What is the duration of Mr. Lane’s expected commute?

1. A) 31.5 minutes
2. B) 27.25 minutes
3. C) 25.5 minutes
4. D) 33.75 minutes

150) What is the probability that Mr. Lane makes it home in under thirty minutes?

1. A) .15
2. B) .35
3. C) .20
4. D) .55

Diff: 2   Page Ref: 507-508

151) What kind of probability is demonstrated if Mr. Lane is asked to predict the duration of his next commute?

1. A) subjective probability
2. B) conjecture probability
3. C) objective probability
4. D) reflexive probability

152) Which of these events are mutually exclusive?

1. A) The duration of Mr. Lane’s commute is less than expected; Mr. Lane’s commute is between twenty and thirty minutes.
2. B) Mr. Lane’s commute is longer than 30 minutes; Mr. Lane’s commute is longer than 40 minutes.
3. C) Mr Lanes commute is between ten and forty minutes; Mr. Lane’s commute is between twenty and thirty minutes.
4. D) Mr. Lane’s commute takes less than ten minutes; Mr Lane’s commute exceeds his expected commute.

Introduction to Management Science, (Taylor)

Chapter 12 Decision Analysis

1) A state of nature is an actual event that may occur in the future.

2) A payoff table is a means of organizing a decision situation, including the payoffs from different decisions given the various states of nature.

3) The maximax criterion results in the maximum of the maximum payoffs.

4) The maximin approach involves choosing the alternative with the highest payoff.

5) Regret is the difference between the payoff from the best decision and all other decision payoffs.

6) The minimax regret criterion minimizes the maximum regret.

7) The minimax regret criterion maximizes the minimum regret.

8) The Hurwicz criterion is a compromise between the maximax and maximin criteria.

9) The Hurwicz criterion is a compromise between the minimax and minimin criteria.

10) The coefficient of optimism is a measure of the decision maker’s optimism.

11) The Hurwicz criterion multiplies the best payoff by the coefficient of optimism.

12) The Hurwicz criterion multiplies the worst payoff by the coefficient of optimism.

13) A dominant decision is one that has a better payoff than another decision under each state of nature.

14) The appropriate criterion is dependent on the risk personality and philosophy of the decision maker.

15) The maximax criterion is optimistic.

16) The maximin criterion maximizes the minimum regret.

17) The minimax criterion minimizes the maximum payoff.

18) Regret and opportunity loss mean the same thing.

19) The equal likelihood criterion assigns a probability of 0.5 to each state of nature.

20) Expected opportunity loss is the expected value of the regret for each decision.

21) When using decision trees, branches with the greatest expected value are selected.

22) A decision tree is a diagram consisting of circular decision nodes, square probability nodes, and branches.

23) Additional information is used to alter the marginal probability of occurrence of an event in Bayesian analysis.

24) A conditional probability is the probability that two events will occur simultaneously.

25) A posterior probability is the likelihood that an event has occurred after the decision maker has reached a decision.

26) Events are mutually exclusive if one, and only one, can occur at a time.

27) The expected value of perfect information divided by the expected value of sample information is the efficiency of perfect information.

28) When the ________ criterion is used, the maximum of the maximum payoffs is selected.

29) When the ________ criterion is used, the maximum of the minimum payoffs is selected

30) ________ is the difference between the payoff from the best decision and all other decision payoffs.

31) The ________ is a compromise between the maximax and the maximin criterion.

32) The ________ is a measure of the decision makers optimism.

33) A(n) ________ decision is one that has a better payoff than another decision under each state of nature.

34) A ________ structures decisions with a series of nodes.

35) The ________ of sample information is the ratio of the expected value of sample information to the expected value of perfect information.

36) When the ________ criterion is used, the decision maker selects the decision alternative that minimizes the maximum regret.

37) A ________ decision tree illustrates a situation requiring a series of decisions.

38) ________ is a measure of personal satisfaciton derived from money.

39) People who forgo a high expected value to avoid a disaster with a low probability are ________.

40) The efficiency of sample information is the ratio of the expected value of sample information to ________.

41) The difference in the expected value with additional information and without additional information is ________.

42) The efficiency of sample information multiplied by the expected value of perfect information is ________.

43) If only one of three events can occur at any given time, the events are ________.

44) If the decision maker receives additional information such that the marginal probabilities of certain events should be modified, these revised probabilites are called ________.

A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.

Weather

Cold    Warm Rainy

S1       S2       S3

Bike:  A1       10        8         6

Hike:  A2       14        15        2

Fish:   A3       7         8         9

45) If the group is optimistic, what decision should they make?

46) If the group is conservative, what decision will they make?

47) If the group chooses to minimize their maximum regret, what activity will they choose?

48) If the probabilities of cold weather (S1), warm weather (S2), and rainy weather (S3) are 0.2, 0.4, and 0.4, respectively, then what decision should be made using the expected value criterion?

49) If the probabilities of cold weather (S1), warm weather (S2), and rainy weather (S3) are 0.2, 0.4, and 0.4, respectively, then what is the EVPI for this situation?

An investor is consider four different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below.

Economic Condition

Poor       Average       Good     Excellent

Investment          (S1)          (S2)          (S3)          (S4)

A                       50              75              20              30

B                       80              15              40              50

C                    -100            300             -50              10

D                       25              25              25              25

50) What decision would be made under maximax?

51) What decision would be made under maximin?

52) What decision would be made under minimax regret?

53) If the probabilities of each economic condition are 0.5, 0.1, 0.35, and 0.05, respectively, what investment would be made using the expected value criterion?

54) If the probabilities of each economic condition are 0.5, 0.1, 0.35, and 0.05, respectively, what is the expected value of perfect information?

A manager has developed a payoff table that indicates the profits associated with a set of alternatives under two possible states of nature.

Alt             S1                S2

1                10                 2

2                -2                 8

3                8                 5

55) If the manager uses maximin as the decision criterion, which of the alternatives should she choose?

56) If the manager uses minimax regret as the decision criterion, which of the alternatives would she choose?

57) Use the expected value criterion to select the best alternative. Assume that the probability of S2 is equal to 0.4.

58) Compute the expected value of perfect information assuming that the probability of S2

is equal to 0.4.

The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues (in thousands) will vary with how well taxpayers comply with the new tax code.

59) If he uses the maximin criterion, how many new workers will he hire?

60) If he uses the minimax regret criterion, how many new workers will he hire?

Diff: 2   Page Ref: 541

Section Heading: Decision Making without Probabilities

Keywords: minimax regret criterion

AACSB: Analytic skills

61) If he thinks the chances of low, medium, and high compliance are 20%, 30%, and 50%, respectively, what are the expected net revenues for the number of workers he will decide to hire?

62) If he thinks the chances of low, medium, and high compliance are 20%, 30%, and 50%, respectively, what is the expected value of perfect information?

A manufacturer must decide whether to build a small or a large plant at a new location. Demand at the location can be either low or high, with probabilities estimated to be 0.4 and 0.6, respectively. If a small plant is built, and demand is high, the production manager may choose to maintain the current size or to expand. The net present value of profits is \$223,000 if the firm chooses not to expand. However, if the firm chooses to expand, there is a 50% chance that the net present value of the returns will be 330,000 and a 50% chance the estimated net present value of profits will be \$210,000. If a small facility is built and demand is low, there is no reason to expand and the net present value of the profits is \$200,000. However, if a large facility is built and the demand turns out to be low, the choice is to do nothing with a net present value of \$40,000 or to stimulate demand through local advertising. The response to advertising can be either modest with a probability of .3 or favorable with a probability of .7. If the response to advertising is modest, the net present value of the profits is \$20,000. However, if the response to advertising is favorable, then the net present value of the profits is \$220,000. Finally, if the large plant is built and the demand happens to be high, the net present value of the profits \$800,000.

63) Draw a decision tree.

64) Draw a decision tree and determine the payoff for each decision and event node. Which alternative should the manufacturer choose?

65) If a student attends every management science class, the probability of passing the course is 0.80; but if the student only attends randomly, then the probability of passing the course is 0.50. If a student fails, he or she can take a makeup exam where the probability of passing is 0.60 if the student has attended every class. This probability of passing the makeup exam drops to 0.10 if the student has attended at random.

Passing the course is worth 5 credits. Full time attendance “costs” 3 credits in terms of energy and time, whereas random attendance “costs” only 1 credit.

Use a decision tree to decide which is the best attendance pattern to adopt. Assume that all failing students take the make up exam and that the payoff for failing is equal to 0.

The quality control manager for ENTA Inc. must decide whether to accept (A1), further analyze (A2), or reject (A3) a lot of incoming material. Assume the following payoff table is available. Historical data indicates that there is 30% chance that the lot is poor quality (S1), 50 % chance that the lot is fair quality (S2), and 20% chance that the lot is good quality (S3).

66) What action would you choose according to maximax criterion?

67) What action would you choose according to maximin criterion?

68) Construct the regret table.

69) What action would you choose according to minimax regret criterion?

70) What action would you choose according to expected value criterion?

71) What is the maximum amount that you would be willing to pay for perfect information?

of perfect information

AACSB: Analytic skills

72) Lucky Lucy is playing the slots in Reno, Nevada, holding her last silver dollar. There are three possible payoffs if she wins: one cherry, \$1; two cherries, \$5; or three cherries, \$50. Anything else on the slot machine loses.

Construct the payoff table for Lucky Lucy.

Napoleon is contemplating four institutions of higher learning as options for a Masters in Business Administration. Each university has strong and weak points and the demand for MBA graduates is uncertain. The availability of jobs, student loans, and financial support will have a significant impact on Napoleon’s ultimate decision. Vanderbilt and Seattle University have comparatively high tuition, which would necessitate Napoleon take out student loans resulting in possibly substantial student loan debt. In a tight market, degrees with that cachet might spell the difference between a hefty paycheck and a piddling unemployment check. Northeastern State University and Texas Tech University hold the advantage of comparatively low tuition but a more regional appeal in a tight job market. Napoleon gathers his advisory council of Kip and Pedro to assist with the decision. Together they forecast three possible scenarios for the job market and institutional success and predict annual cash flows associated with an MBA from each institution. All cash flows in the table are in thousands of dollars.

 School Scenario 1 Scenario 2 Scenario 3 Vanderbilt 95 20 -10 Texas Tech 55 60 60 Seattle 90 10 80 Northeastern State 65 50 60

73) Kip tends to be extremely optimistic. Which decision making criterion would he naturally select and what conclusion would he recommend to Napoleon? Why?

74) Pedro is extremely pessimistic. Which decision making criterion would he naturally select and what conclusion would he recommend to Napoleon? Why?

75) Napoleon doesn’t know what to think, since he has no idea which scenario will happen. Which criterion is he well-suited for and what is his decision?

76) Summer bursts into the meeting and announces that there’s another way to consider the issue. Since Napoleon will have to live with his choice for the rest of his life, he might consider selecting the alternative that will cause him the least pain in hindsight when he compares his outcome with what he might have gained. Which criterion is she talking about, what is the best school for this criterion, and why?

77) Napoleon’s Uncle Rico believes that the scenarios are not necessarily equally likely, and suggests that the likelihood of occurrence of Scenario 2 is 0.4 and the likelihood of occurrence of Scenarios 1 and 3 are both 0.3. What two criteria are most appropriate and what is the resulting decision?

78) Consider the following decision tree.

What is the expected value at node 4?

79) Consider the following decision tree.

What is the value associated with node 3?

80) Consider the following decision tree.

Which decision, A or B, is best? What is the expected value of this decision?

81) The maximax criterion results in the

1. A) maximum of the minimum payoffs.
2. B) maximum of the maximum payoffs.
3. C) minimum of the maximum payoffs.
4. D) minimum of the minimum payoffs.

82) The maximin criterion results in the

1. A) minimum of the maximum payoffs.
2. B) maximum of the maximum payoffs.
3. C) maximum of the minimum payoffs.
4. D) minimum of the minimum payoffs.

83) Regret is the difference between the payoff from the

1. A) best decision and all other decision payoffs.
2. B) worst decision and all other decision payoffs.
3. C) best decision and the worst decision payoffs.
4. D) none of the above

84) The ________ minimizes the maximum regret.

1. A) maximax regret criterion
2. B) minimax regret criterion
3. C) minimin regret criterion
4. D) maximin regret criterion

85) The minimax regret criterion

1. A) maximizes the minimum regret.
2. B) minimizes the minimum regret.
3. C) minimizes the maximum regret.
4. D) maximizes the maximum regret.

86) Determining the worst payoff for each alternative and choosing the alternative with the best worst is called

1. A) maximin.
2. B) minimin.
3. C) maximax.
4. D) minimax.

87) The maximin approach to decision making refers to

1. A) minimizing the maximum return.
2. B) maximizing the minimum return.
3. C) maximizing the maximum return.
4. D) minimizing the minimum return.

88) The term opportunity loss is most closely related to

1. A) maximin regret.
2. B) maximax regret.
3. C) minimax regret.
4. D) minimin regret.

89) The Hurwicz criterion is a compromise

1. A) between the maximin and minimax criteria.
2. B) between the minimax and maximax criteria.
3. C) between the maximax and maximin criteria.
4. D) none of the above

90) The Hurwicz criterion multiplies the

1. A) best payoff by the coefficient of optimism.
2. B) worst payoff by the coefficient of optimism.
3. C) best payoff by the worst payoff.
4. D) none of the above

91) The basic decision environment categories are

1. A) certainty.
2. B) risk.
3. C) uncertainty.
4. D) all of the above

Napoleon is contemplating four institutions of higher learning as options for a Masters in Business Administration. Each university has strong and weak points and the demand for MBA graduates is uncertain. The availability of jobs, student loans, and financial support will have a significant impact on Napoleon’s ultimate decision. Vanderbilt and Seattle University have comparatively high tuition, which would necessitate Napoleon take out student loans resulting in possibly substantial student loan debt. In a tight market, degrees with that cachet might spell the difference between a hefty paycheck and a piddling unemployment check. Northeastern State University and Texas Tech University hold the advantage of comparatively low tuition but a more regional appeal in a tight job market. Napoleon gathers his advisory council of Kip and Pedro to assist with the decision. Together they forecast three possible scenarios for the job market and institutional success and predict annual cash flows associated with an MBA from each institution. All cash flows in the table are in thousands of dollars.

 School Scenario 1 Scenario 2 Scenario 3 Vanderbilt 95 20 -10 Texas Tech 55 60 60 Seattle 90 10 80 Northeastern State 65 50 60

92) Under which decision making criterion is Vanderbilt University the optimal choice?

1. A) maximax
2. B) maximin
3. C) minimax regret
4. D) equally likely

93) Under which decision making criterion is Texas Tech University the optimal decision?

1. A) maximax
2. B) maximin
3. C) minimax regret
4. D) equally likely

94) Under which criterion is Seattle University the optimal decision?

1. A) maximax
2. B) maximin
3. C) minimax regret
4. D) equally likely

95) Under which criterion is Northeastern State University the optimal decision?

1. A) maximax
2. B) maximin
3. C) minimax regret
4. D) equally likely

96) Suppose that the likelihood for each of the scenarios 1 through 3 is 0.3, 0.4, and 0.3, respectively. What is the optimal decision under the expected opportunity loss criterion?

1. A) Vanderbilt University
2. B) Texas Tech University
3. C) Seattle University
4. D) Northeastern State University

97) The basic decision environment categories are

1. A) certainty and risk.
2. B) risk and uncertainty.
3. C) certainty and uncertainty.
4. D) certainty, uncertainty and risk.

98) The Hurwicz criterion

1. A) multiplies the worst payoff by one minus the coefficient of optimism.
2. B) multiplies the best payoff by one minus the coefficient of optimism.
3. C) is a compromise between the minimax and maximin criteria.
4. D) all of the above

99) The appropriate criterion is dependent on

1. A) the risk personality of the decision maker
2. B) the number of nodes in the decision tree.
3. C) the magnitude of the payoffs.
4. D) none of the above

100) The ________ is a measure of the decision maker’s optimism.

1. A) equal likelihood criterion
2. B) dominant decision
3. C) coefficient of optimism
4. D) opportunity loss

101) The ________ multiplies the decision payoff for each state of nature by an equal weight.

1. A) dominant decision
2. B) coefficient of optimism
3. C) equal likelihood criterion
4. D) none of the above

102) A ________ is one that has a better payoff than another decision under each state of nature.

1. A) coefficient of optimism
2. B) equal likelihood criterion
3. C) dominant decision
4. D) none of the above

103) A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

The maximax strategy is

2. B) Rent.
3. C) Lease.
4. D) Brisk.

104) A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

The maximin strategy is

2. B) Rent.
3. C) Lease.
4. D) Brisk.

105) A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

The equal likelihood criterion strategy is

2. B) Rent.
3. C) Lease.
4. D) Brisk.

106) A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

If the probability of brisk business is .40 and for slow business is .60, the expected value of perfect information is:

1. A) 12
2. B) 55
3. C) 57
4. D) 69

107) The ________ is computed by multiplying each decision outcome under each state of nature by the probability of its occurrence.

1. A) expected value
2. B) expected value of perfect information
3. C) expected opportunity loss
4. D) none of the above

108) The ________ is the expected value of the regret for each decision.

1. A) expected value
2. B) expected opportunity loss
3. C) expected value of perfect information
4. D) none of the above

109) A tabular presentation that shows the outcome for each decision alternative under the various possible states of nature is called a

1. A) decision tree.
2. B) payoff table.
3. C) feasible region.
4. D) payback matrix.

110) The ________ is the maximum amount a decision maker would pay for additional information.

1. A) expected opportunity loss
2. B) expected value
3. C) expected value of perfect information
4. D) bid price

111) A decision tree is a diagram consisting of

1. A) branch angles that vary as likelihoods increase.
2. B) triangle probability nodes.
3. C) branches representing decision alternatives.
4. D) perfect information.

112) In ________ additional information is used to alter the marginal probability of the occurrence of an event.

1. A) Bayesian analysis
2. B) decision analysis
3. C) probability analysis
4. D) decision making under certainty

113) A ________ probability is the probability that an event will occur given that another event has already occurred.

1. A) posterior
2. B) conditional
3. C) marginal
4. D) low

114) A ________ probability is the altered marginal probability of an event based on additional information.

1. A) marginal
2. B) conditional
3. C) posterior
4. D) none of the above

115) The efficiency of sample information is the ratio of the expected value of sample information to the

1. A) expected value of perfect information.
2. B) expected value.
3. C) utilization rate.
4. D) coefficient of optimism.

116) The expected value of sample information

1. A) is never more than EVPI.
2. B) can be greater or less than EVPI.
3. C) can be positive or negative.
4. D) is equivalent to the EVPI.

117) People who forgo a high expected value to avoid a disaster with a low probability are

1. A) risk takers.
2. B) risk averters.
3. C) risk calculators.
4. D) risk predictors.

118) People who take a chance on a bonanza with a very low probability of occurrence in lieu of a sure thing are

1. A) risk takers.
2. B) risk averters.
3. C) risk calculators.
4. D) risk predictors.

119) Utiles are units of ________ measures of utility.

1. A) quantitative
2. B) objective
3. C) subjective
4. D) qualitative

A small entrepreneurial company is trying to decide between developing two different products that they believe they can sell to two potential companies, one large and one small. If they develop Product A, they have a 50% chance of selling it to the large company with annual purchases of about 20,000 units. If the large company won’t purchase it, then they think they have an 80% chance of placing it with a smaller company, with sales of 15,000 units. On the other hand if they develop Product B, they feel they have a 40% chance of selling it to the large company, resulting in annual sales of about 17,000 units. If the large company doesn’t buy it, they have a 50% chance of selling it to the small company with sales of 20,000 units.

120) What is the probability that Product A will being purchased by the smaller company?

1. A) 0.8
2. B) 0.5
3. C) 0.4
4. D) 0.2

121) What is the probability that Product B will being purchased by the smaller company?

1. A) 0.8
2. B) 0.5
3. C) 0.4
4. D) 0.3

122) How many units of Product A can they expect to sell?

1. A) 20,000
2. B) 17,000
3. C) 16,000
4. D) 15,000

Introduction to Management Science, (Taylor)

Chapter 14 Simulation

1) In computer mathematical simulation, a system is replicated with a mathematical model that is analyzed with the computer.

2) Monte Carlo is a technique for selecting numbers randomly from a probability distribution.

3) The Monte Carlo process is analogous to gambling devices.

4) In the Monte Carlo process, values for a random variable are generated by sampling from a probability distribution.

5) A long period of real time can be represented by a short period of simulated time.

6) Random numbers are equally likely to occur.

7) Simulation results will always equal analytical results if 30 trials of the simulation have been conducted.

8) It’s often difficult to validate that the results of a simulation truly replicate reality.

Diff: 1   Page Ref: 642

Section Heading: The Monte Carlo Process

Keywords: simulation results

9) Simulation applies mathematical models to determine optimal solutions to business problems.

10) Validation of a simulation model occurs when the true steady state average results have been reached.

11) Random numbers generated by a mathematical process instead of a physical process are pseudorandom numbers.

12) Random numbers are typically generated on the computer using a numerical technique.

13) A table of random numbers must be normally distributed and efficiently generated.

14) When using Excel to simulate a system, it is necessary to compute only the probability (relative frequency) distribution.

15) Excel can only be used to simulate systems that can be represented by continuous random variables.

16) In Excel the VLOOKUP function is used to determine values for continuous random variables.

17) Developing the cumulative probability distribution helps to determine random number ranges.

18) Starting conditions have no impact on the validity of a simulation model.

19) Simulations should always be started with an empty system.

20) Manual simulation is limited because of the amount of real time required to simulate even one trial.

21) Applications of simulation models reflecting continuous distributions are more common than those of models employing discrete distributions.

22) In a continuous probability function, the area under the curve represents the probability of occurrence of the random variable.

23) Cumulative probabilities are analogous to the discrete ranges of random numbers used in the Monte Carlo process.

24) Integrating a function from zero to any value of a random variable x is an important step in determining the cumulative probability of that value of x.

25) ________ is a technique for selecting numbers randomly from a probability distribution.

26) Developing the ________ probability distribution helps to determine random number ranges.

27) Random numbers of a mathematical process instead of a physical process are ________ numbers.

28) Simulation models must be ________ to make sure they are accurately replicating the system being simulated.

29) A table of random numbers must be ________ distributed, efficiently generated, and absent of patterns.

30) The ________ command is used in generating the random numbers with Excel.

31) In order to determine the value of discrete demand in a simulation model using Excel, the ________ function is used to associate a specific value of demand with a random number.

32) ________ is a risk analysis and forecasting program that uses Monte Carlo simulation.

33) ________, ________, and ________ are common applications of simulation.

34) In the Monte Carlo process, values for a random variable are generated by sampling from a(n) ________.

35) A long period of real time is represented by a short period of ________.

36) The Monte Carlo process is analogous to and derives its name from ________.

37) ________ are numbers equally likely to be chosen from a large population of numbers.

38) A random number table features numbers that are derived from a(n) ________ process.

39) Consider the following distribution and random numbers:

If a simulation begins with the first random number, what would the first simulation value would be ________.

The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.

40) Determine the drying time for these 5 random numbers: 0.13, 0.09, 0.19, 0.81, and 0.12.

41) Determine the drying time for these 5 random numbers: 0.53, 0.95, 0.97, 0.96, and 0.07.

42) The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.

What is the average drying time if you simulate 10 trials using these random numbers:

0.13, 0.09, 0.19, 0.81, 0.12, 0.53, 0.95, 0.97, 0.96, and 0.07.

43) Determine the random number ranges for the data set (start with 00).

Demand   Frequency

5                 0.15

6                  0.3

7                 0.25

8                 0.15

9                 0.15

Diff: 3   Page Ref: 640

Section Heading: The Monte Carlo Process

Keywords: random number ranges

AACSB: Analytic skills

44) Given the following random number ranges and the following random number sequence: 62, 13, 25, 40, 86, 93, determine the average demand for the following distribution of demand.

 Demand Random Number Ranges 5 00-14 6 15-44 7 45-69 8 70-84 9 85-99

45) If f(x) = 2x, what is the equation for generating x, given the random number r?

46) The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.

Compute the mean drying time.

47) A normal distribution has a mean of 500 and a standard deviation of 50. A manager wants to simulate two values from this distribution and has drawn these random numbers: -0.6 and 1.4. What are the two values, respectively?

48) The number of cars arriving at Joe Kelly’s oil change and tune-up place during the last 200 hours of operation is observed to be the following:

Determine the probability distribution of car arrivals.

49) The number of cars arriving at Joe Kelly’s oil change and tune-up place during the last 200 hours of operation is observed to be the following:

Based on the above frequencies, use two-digit random numbers, start with random number 00, and determine the random number ranges for the data set given above.

50) Consider the following manual simulation of machine breakdowns and repair.

 Breakdowns Time between breakdowns, x (weeks) Repair time, y (days) Cost (\$2,000 y) 1 4 1 \$2000 2 5.7 2 \$4000 3 5.5 2 \$4000 4 2.5 1 \$2000 5 5.2 2 \$4000 6 5.8 2 \$4000 7 1.6 1 \$2000 8 2.3 2 \$4000 9 1.2 2 \$4000 10 3.3 2 \$4000

What operating charactistics can be obtained from this simulation?

51) George Pourbabaee owns a gas station. The cars arrive at the gas station according to the following inter-arrival time distribution. The time to service a car is given by the following service time distribution.

 Interarrival time (in minutes) P(X) Random Numbers Service Time (in minutes) P (X) Random Numbers 4 .35 00-34 2 .30 00-29 7 .25 35-59 4 .40 30-69 10 .30 60-89 6 .20 70-89 20 .10 90-99 8 .10 90-99

Using the following random number sequence: 92, 44, 15, 97, 21, 80, 38, 64, 74, 08, estimate the average customer waiting time, average idle time of the assistant, and the average time a car spends in the system.

52) An answering service for a doctor’s office wants to evaluate the service by simulation calls. They used past data to determine the distributions for the time between calls and the time spent on the phone with patients.

Use the table below to manually simulate 8 calls. The time of the call and the service time have already been determined.

 Customer Number Time of Call Time call answered Service Time Time call ends Customer Wait Time Operator Wait Time 1 15 15 25 40 0 15 2 45 45 25 70 0 5 3 70 15 4 95 45 5 125 15 155 6 150 35 7 175 190 25 15 0 8 205 25 240 10 0

Calculate the average waiting time per customer.

Calculate the utilization of the operator.

A graduate research assistant “moonlights” at the short order counter in the student union snack bar in the evenings. He is considering asking for help taking orders, but needs to convince the management that they should hire another student. Because he is taking a simulation class, he thinks it may be the perfect way to convince management to hire more help if he can show that customers have to wait a long time. When a customer arrives, he takes their order and their payment, prepares the food, gives it to the customer, and then takes the order from the next person in line. If someone arrives while he’s cooking an order, they have to wait until he’s completed the current order. He is working on the simulation and a portion is shown below.

53) Complete the table below and determine the average customer wait time.

 Customer Number Time of Arrival Time Order Taken Order Prep Time Customer Receives Food Customer Wait Time 1 2 2 4 6 0 2 14 14 7 3 19 6 4 28 8 5 33 4

54) Complete the table and determine the average customer waiting time and the utilization of the cook.

 Customer Number Time of Arrival Time Order Taken Order Prep Time Customer Receives Food Customer Wait Time Cook “Idle” TIme 1 2 2 4 6 0 2 2 14 14 7 3 19 6 4 28 8 5 33 4

Complete the table and determine the average customer waiting time and the utilization of the cook.

55) Assume that order prep time is based on the following distribution:

 Prep Time Probability 3 .10 4 .20 5 .25 6 .20 7 .15 8 .10

Complete the following table given that the random numbers for order prep time for customers 3, 4, and 5 are 62, 93, and 26, respectively.

 Arrival Number Time of Arrival Time Order Taken Order Prep Time Customer Receives Food Customer Wait Time Cook “Idle” Time 1 1 1 4 5 0 1 2 5 5 7 12 0 0 3 7 4 10 5 18

What is the average customer waiting time and the graduate student’s utilization?

A business professor wishes to model the duration of his commute through the busy streets of Bangalore. He decides to model it based on the number of auto-rickshaws that he passes during the first ten minutes of the drive. The continuous probability distribution 7x – 2 serves as a good model.

56) What is the integral from 0 to 4 for this distribution?

57) If the first four random numbers are 17, 33, 64, and 8, what is the average number of weeks?

58) If each contract is worth \$4000 but it costs \$200 per week to work on a contract, what is the profit resulting from a simulation drawing of the numbers 72, 36, 8, 71, and 94?

59) If the ten numbers generated are 87, 84, 99, 18, 81, 75, 32, 87, 46, and 35, what is the resultant expected average completion time?

60) If each contract is worth \$5000 but it costs \$300 per week to work on a contract, what is the profit resulting from a simulation drawing of the numbers 72, 36, 8, 71, and 94 to represent contract durations?

A newsboy sells newspapers and his goal is to maximize profit. He kept a record of his sales for 125 days with the following result:

 Newspapers demand per day Number of days 15 10 16 20 17 42 18 31 19 12 20 10 Total 125

His ordering policy is to order an amount each day that is equal to the previous day’s demand.

A newspaper costs the carrier 50 cents and he sells it for \$1.00. Unsold papers are returned and he receives 25 cents (for a loss of 25 cents).

61) Develop the cumulative distribution table and the corresponding random numbers.

 Newspapers demanded per day Number of Days Probability Cumulative Probability 15 10 16 20 17 42 18 31 19 12 20 10 Total

62) Use the information and random numbers given in the table below to simulate the sale of newspapers for 10 days.

 Day Demand Random Number Quantity Ordered Sales Unsatisfied Demand Unsold Papers 1 .78 18 2 .43 3 .93 4 .87 5 .48 6 .84 7 .87 8 .27 9 .20 10 .52

After completing the simulation, determine his total revenue for the ten days as well as monetary losses that result from unmet demand and unsold papers.

63) Analogue simulation replaces a physical system with an analogous physical system that is ________ to manipulate.

1. A) harder
2. B) easier
3. C) equally difficult
4. D) more expensive

64) ________ is a technique for selecting numbers randomly from a probability distribution.

1. A) Marseille
2. B) Monaco
3. C) Monte Carlo
4. D) Analogue simulation

65) In the Monte Carlo process, values for a random variable are generated by ________ a probability distribution.

1. A) sampling from
2. B) running
3. C) integrating
4. D) implementing

66) The ________ process is analogous to gambling devices.

1. A) Simulation
2. B) Monte Carlo
3. C) Monaco
4. D) none of the above

67) ________ numbers are numbers derived from a mathematical process that appear to be random.

1. A) Random
2. B) Pseudorandom
3. C) Randomized
4. D) Semi-random

68) Pseudorandom numbers exhibit a ________ in order to be considered truly random.

1. A) limited number of possible outcomes
2. B) uniform distribution
3. C) detectable pattern
4. D) detectable run of certain numbers

69) ________ is not part of a Monte Carlo simulation.

1. A) Analyzing results
2. B) Analyzing a real problem
3. C) Finding an optimal solution
4. D) Evaluating the results

70) A seed value is a(n)

1. A) steady state solution of a simulation experiment.
2. B) number used to start a stream of random numbers.
3. C) first run of a simulation model.
4. D) analytic solution of a simulation experiment.

71) In assigning random numbers to probabilistic events in a simulation,

1. A) several events are associated with the same random number.
2. B) every random number is associated with a particular event.
3. C) every event is associated with the same random number.
4. D) the events dictate the seed number of the random number stream.

72) ________ are the values that express the state of the system being modeled at the beginning of the Monte Carlo simulation.

1. A) Outputs
2. B) Random events
3. C) Initial conditions
4. D) Random numbers

73) Simulation does not usually provide recommended decisions. Instead it provides

1. A) operating characteristics.
2. B) optimal solutions.
3. C) realistic results.
4. D) system parameters.

74) For the following frequency distribution of demand, the random number 0.23 would be interpreted as a demand of:

1. A) 0
2. B) 1
3. C) 2
4. D) 3

Consider the following frequency of demand and random numbers:

Random numbers: 0.13, 0.81, 0.53.

75) If the simulation begins with the first random number, the simulated value for demand would be:

1. A) 0
2. B) 1
3. C) 2
4. D) 3

76) If the simulation begins with the second random number, the simulated value for demand would be:

1. A) 1
2. B) 2
3. C) 3
4. D) 4

77) If the simulation begins with the third random number, the simulated value for demand would be:

1. A) 0
2. B) 1
3. C) 2
4. D) 3
5. E) 4

78) Which of the following would not be considered a limitation of simulation modeling?

1. A) Models are typically unstructured.
2. B) Validation of simulation models can be difficult.
3. C) The cost of building simulation can be prohibitive.
4. D) Simulation allows flexibility in analyzing systems.

79) Simulations are normally done

1. A) manually.
2. B) in a casino.
4. D) on the computer.

80) Random numbers generated by a ________ process instead of a ________ process are pseudorandom numbers.

1. A) physical, physical
2. B) physical, mathematical
3. C) mathematical, physical
4. D) mathematical, mathematical

81) A table of random numbers must be

1. A) in descending order.
2. B) efficiently generated.
3. C) normally distributed.
4. D) in ascending order.

82) Developing the cumulative probability distribution helps to determine

1. A) simulation numbers.
2. B) data sets.
3. C) random number ranges.
4. D) mean of the distribution.

A graduate research assistant “moonlights” at the short order counter in the student union snack bar in the evenings. He is considering asking for help taking orders, but needs to convince the management that they should hire another student. Because he is taking a simulation class, he thinks it may be the perfect way to convince management to hire more help if he can show that customers have to wait a long time. When a customer arrives, he takes their order and their payment, prepares the food, gives it to the customer, and then takes the order from the next person in line. If someone arrives while he’s cooking an order, they have to wait until he’s completed the current order. He has simulated 5 orders.

 Customer Number Time of Arrival Time Order Taken Order Prep Time Customer Receives Food Customer Wait Time 1 2 2 4 6 0 2 14 14 7 3 19 6 4 28 8 5 33 4

83) Average customer waiting time is:

1. A) 1 minute
2. B) 2 minutes
3. C) 2.5 minutes
4. D) 3 minutes

84) Average utilization is:

1. A) 67%
2. B) 72.5%
3. C) 83.4%
4. D) 95%

85) ________ simulation is limited because of the amount of real time required to simulate even one trial.

1. A) Manual
2. B) Monte Carlo
3. C) Monaco
4. D) Any kind of

86) If the probability of an event is 0.36, what random number range specifies this properly?

1. A) 0.10 – 0.20
2. B) 0.20 – 0.30
3. C) 0.30 – 0.40
4. D) 0.40 – 0.50

87) Sometimes manual simulation of several trials is ________ way to validate a simulation.

1. A) a good
3. C) no
4. D) the only

88) Unlike optimization models, simulation provides

1. A) recommendations.
2. B) operating characteristics.
3. C) suggestions.
4. D) solutions .

89) A limitation of simulation is that

1. A) models are typically well-structured and must be developed for problems that are also well-structured.
2. B) it is usually possible to realistically validate simulation results.
3. C) model building is costly and time-consuming.
4. D) it is more difficult to manipulate the elements of a computer simulation than the actual system.

The U.S. Department of Agriculture estimates that the yearly yield of limes per acre is distributed as follows:

 Yield, bushels per acre Probability 350 .10 400 .18 450 .50 500 .22

The estimated average price per bushel is \$16.80.

90) What is the expected yield of the crop?

1. A) 425
2. B) 442
3. C) 440
4. D) 475

91) Use the following random numbers to simulation crop yield for 10 years: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81. What is the estimated crop yield from the simulation?

1. A) 425
2. B) 442
3. C) 440
4. D) 475

A bakery is considering hiring another clerk to better serve customers. To help with this decision, records were kept to determine how many customers arrived in 10-minute intervals. Based on 100 10-minute intervals, the following probability distribution and random number assignments developed.

 Number of Arrivals Probability Random numbers 6 .1 .01 – .10 7 .3 .11 – .40 8 .3 .41 – .70 9 .2 .71 – .90 10 .1 .91 – .00

92) Suppose the next three random numbers were .18, .89 and .67. How many customers would have arrived during this 30-minute period?

1. A) 22
2. B) 23
3. C) 24
4. D) 25

93) Suppose the next three random numbers were .08, .50 and .69. How many customers would have arrived during this 30-minute period?

1. A) 22
2. B) 23
3. C) 24
4. D) 25

94) Suppose the next three random numbers were .11, .42 and .84. Use these values to simulate arrivals into the bakery and determine the average number of arrivals per 10-minute period based on these occurrences. The average number of arrivals per 10-minute period is:

1. A) 6
2. B) 7
3. C) 8
4. D) 9

Two hundred simulation runs were completed using the probability of a machine breakdown from the table below. The average number of breakdowns from the simulation trials was 1.93 with a standard deviation of 0.20.

 No. of breakdowns per week Probability Cumulative probability 0 .10 .10 1 .25 .35 2 .36 .71 3 .22 .93 4 .07 1.00

95) What is the probability of 2 or fewer breakdowns?

1. A) .25
2. B) .35
3. C) .36
4. D) .71

96) What is the probability that there are more than 3 breakdowns?

1. A) .07
2. B) .10
3. C) .22
4. D) .25

97) Construct a 95% confidence interval for the average number of machine breakdowns.

1. A) 1.896 to 1.938
2. B) 1.902 to 1.958
3. C) .1.877 to 1.943
4. D) 1.907 to 1.953

98) A 95% confidence interval is (54.5, 57.5) based on a sample size of 25. What is the sample standard deviation?

1. A) 3.826
2. B) 19.132
3. C) 8.973
4. D) 11.646

99) What is the 95% confidence interval width for a sample with a mean of 50 and a standard deviation of 14 based on 75 observations?

1. A) (44.13, 55.87)
2. B) (46.83, 53.17)
3. C) (40.67, 59.32)
4. D) (48.22, 51.78)

100) The use of simulation to determine the impact of projects such as nuclear power plants, reservoirs and dams is known as

1. A) public service operation.
2. B) environmental and resource analysis.
3. C) cost benefit analysis.
4. D) project management.

101) The use of simulation to analyze airport operations, and fire or police department operations are known as

1. A) public service operation.
2. B) environmental and resource analysis.
3. C) cost benefit analysis.
4. D) operations management.

Introduction to Management Science, (Taylor)

Chapter 15 Forecasting

1) A trend is a gradual, long-term, up-or-down movement of demand.

Diff: 1   Page Ref: 690

Keywords: trend, forecasting components

2) A seasonal pattern is an up-and-down repetitive movement within a trend occurring periodically.

Diff: 1   Page Ref: 690

Keywords: seasonal pattern, forecasting components

3) Random variations are movements that are not predictable and follow no pattern.

Diff: 2   Page Ref: 690

Keywords: random variations, forecasting components

4) The basic types of forecasting methods include time series, regression, and qualitative methods.

Diff: 2   Page Ref: 691

Keywords: types of forecasting methods

5) Time series is a category of statistical techniques that uses historical data to predict future behavior.

Diff: 1   Page Ref: 691

Keywords: time series analysis

6) Regression methods attempt to develop a mathematical relationship between the item being forecast and factors that cause it to behave the way it does.

Diff: 2   Page Ref: 691

Keywords: regression methods

7) Qualitative methods use management judgment, expertise, and opinion to make forecasts.

Diff: 2   Page Ref: 691

Keywords: qualitative methods

8) Qualitative methods are the least common type of forecasting method for the long-term strategic planning process.

Diff: 1   Page Ref: 691

Keywords: qualitative methods

9) A cycle is an up-or-down movement in demand that repeats itself in less than 1 year.

Diff: 1   Page Ref: 690

Keywords: regression methods

10) Seasonal patterns are observed only during the four seasons – winter, spring, summer, and fall.

Diff: 1   Page Ref: 690

Keywords: time series methods

11) The Delphi method develops a consensus forecast about what will occur in the future.

Diff: 2   Page Ref: 693

Keywords: Delphi method, qualitative methods

12) Technological forecasting helps determine the technological feasibility of new products by surveying large numbers of consumers.

Diff: 1   Page Ref: 693

Keywords: technological forecasting

13) Irregular variations exhibit no pattern.

Diff: 1   Page Ref: 690

Keywords: forecasting components, irregular variation

14) Data cannot exhibit both trend and cyclical patterns.

Diff: 1   Page Ref: 690

Keywords: forecasting components, trend, cyclical

15) Time series methods assume that what has occurred in the past will continue to occur in the future.

Diff: 1   Page Ref: 693

Keywords: time series methods

16) Moving averages are good for stable demand with no pronounced behavioral patterns.

Diff: 2   Page Ref: 693

Keywords: moving averages

17) Longer-period moving averages react more slowly to recent demand changes than do shorter-period moving averages.

Diff: 2   Page Ref: 695

Keywords: moving averages

AACSB: Analytic skills

18) Shorter-period moving averages react more slowly to recent demand changes than do longer-period moving averages.

Diff: 2   Page Ref: 695

Keywords: moving averages

AACSB: Analytic skills

19) In a weighted moving average, weights must sum to 1.

Diff: 1   Page Ref: 696

Keywords: moving averages, weighted moving average, time series methods

20) Adjusted exponential smoothing is an exponential smoothing forecast adjusted for seasonality.

Diff: 1   Page Ref: 700

21) If average forecast error is positive, it indicates that the forecast is biased high.

Diff: 2   Page Ref: 708

Keywords: forecast error

AACSB: Analytic skills

22) Regression is used to relate one variable to one or more variables.

Diff: 1   Page Ref: 713

Keywords: regression methods, linear regression

23) The dependent variable in linear regression is usually designated as the x variable.

Diff: 2   Page Ref: 713

Keywords: regression methods, linear regression

24) In the regression equation y=a+bx, the slope of the equation is x.

Diff: 2   Page Ref: 713

Keywords: regression methods, linear regression

25) Correlation measures the strength of relationship between the x and y variables and the closer it is to 1 or -1, the greater the proof that the level of x determines the level of y.

Diff: 2   Page Ref: 715

Keywords: regression methods, linear regression

26) The coefficient of determination provides a measure of how the level of the independent variable in a regression equation explains the level of the dependent variable in the equation.

Diff: 2   Page Ref: 713

Keywords: regression methods, linear regression

27) ________ is a gradual, long-term, upward or downward movement of demand.

Diff: 2   Page Ref: 690

Keywords: trend

28) A(n) ________ forecast typically encompass a period longer than one year.

Diff: 2   Page Ref: 690

Keywords: long range forecasts

29) Daily operations are assisted by ________-range forecasting

Diff: 1   Page Ref: 690

Keywords: short range forecasts

30) Unpredictable movements in demand that follow no pattern are ________.

Diff: 1   Page Ref: 690

Keywords: forecasting components, irregular variation

31) The major types of forecasting methods are ________, ________, and ________.

Diff: 1   Page Ref: 691

Keywords: forecasting methods

32) Knowledgeable individuals bring their opinions to bear in ________, a qualitative method of forecasting.

Diff: 1   Page Ref: 693

Keywords: Delphi method, qualitative methods

33) A long-term wave in a demand pattern that undulates gracefully over a period of greater than a year is a(n) ________.

Diff: 1   Page Ref: 690

Keywords: forecasting components, trend, cyclical

34) ________ error is the sum of the forecast errors.

Diff: 2   Page Ref: 708

Keywords: medium range forecasts

35) A(n) ________ forecast encompasses the immediate future, is concerned with daily activities of the firm and does not go beyond one or two months in to the future.

Diff: 2   Page Ref: 690

Keywords: short range forecasts

36) A(n) ________ is an up-and-down repetitive movement within a trend occurring periodically.

Diff: 2   Page Ref: 690

Keywords: seasonal pattern, forecasting components

37) ________ relates demand to two or more independent variables.

Diff: 2   Page Ref: 719

Keywords: multiple linear regression analysis

38) One problem with multiple regression is ________, which is a measure of the amount of “overlapping” information about the dependent variable that’s provided by several independent variables.

Diff: 2   Page Ref: 722

Keywords: simple exponential smoothing

39) Exponential smoothing forecasts are more sensitive or reactive to the changes in demand as the value of the smoothing constant, α, ________.

Diff: 2   Page Ref: 698

Keywords: simple exponential smoothing

AACSB: Analytic skills

40) The closer the value of α is to zero, the ________ will be the dampening or smoothing effect.

Diff: 2   Page Ref: 698

Keywords: simple exponential smoothing

AACSB: Analytic skills

41) ________ measures the strength of the relationship between two variables.

Diff: 2   Page Ref: 716

Keywords: correlation, regression methods, linear regression model

42) The ________ is the percentage of variation in the dependent variable that results from the independent variable.

Diff: 2   Page Ref: 716

Keywords: coefficient of determination, reg methods, linear reg model

AACSB: Analytic skills

43) Longer-period moving averages react more ________ to recent demand changes than do shorter period moving averages.

Diff: 2   Page Ref: 694

Keywords: moving average method

AACSB: Analytic skills

44) ________ are the movements or fluctuation in demand that exhibit no pattern and occur on a random basis.

Diff: 2   Page Ref: 690

Keywords: forecasting components, irregular variation

45) The ________ is the sum of the absolute value of forecasting errors divided by the number of periods in which a forecast was made.

Diff: 1   Page Ref: 706

46) The ________ is the average of the sum of the squared errors.

Answer: MSE or mean squared error

Diff: 1   Page Ref: 708

Keywords: forecast error, MSE

47) MAPD measures ________.

Answer: the absolute error as a percentage of the actual (demand) data

Diff: 2   Page Ref: 707

Keywords: forecast error, MAPD

48) ________ is a type of exponential smoothing that can also include trend.

Diff: 1   Page Ref: 700

Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame:

49) Compute a 3-period moving average for period 4.

Diff: 2   Page Ref: 694

Keywords: moving averages, time series methods

AACSB: Analytic skills

50) Compute a 3-period moving average for period 6.

Diff: 2   Page Ref: 694

Keywords: moving averages, time series methods

AACSB: Analytic skills

51) Compute a 3-period moving average for period 7.

Diff: 2   Page Ref: 694

Keywords: moving averages, time series methods

AACSB: Analytic skills

52) Compute a 5-period moving average for period 6.

Diff: 3   Page Ref: 694

Keywords: moving averages, time series methods

AACSB: Analytic skills

53) Compute a 5-period moving average for period 7.

Diff: 3   Page Ref: 694

Keywords: moving averages, time series methods

AACSB: Analytic skills

54) Daily highs in Sacramento for the past week (from least to most recent) were:

95, 102, 101, 96, 95, 90 and 92. Develop a forecast for today using a 2-day moving average.

Diff: 1   Page Ref: 694

Keywords: moving average method

AACSB: Analytic skills

55) Daily highs in Sacramento for the past week (from least to most recent) were:

95, 102, 101, 96, 95, 90 and 92. Develop a forecast for today using a 3-day moving average.

Diff: 1   Page Ref: 694

Keywords: moving average method, forecast error

AACSB: Analytic skills

56) Daily highs in Sacramento for the past week (from least to most recent) were:

95, 102, 101, 96, 95, 90 and 92. Develop a forecast for today using a weighted moving average, with a weights of .6, .3, and .1, where the highest weights are applied to the most recent data.

Answer: 91.7 = .6(92) + .3(90) + .1(95)

Diff: 2   Page Ref: 696

Keywords: weighted moving average

AACSB: Analytic skills

Given the following data on hotel check-ins for a 6-month period:

July:                70 rooms

August:           105 rooms

September:      90 rooms

October:          120 rooms

November:      110 rooms

December:       115 rooms

57) What is the 3-month moving average forecast for January?

Diff: 2   Page Ref: 694

Keywords: moving averages, time series methods

AACSB: Analytic skills

58) With alpha = 0.2, what is the simple exponential smoothing forecast for October? Assume the forecast for July was 80 rooms.

July          70             80

Aug          105           78

Sept         90             83.4

Oct           120           84.72

Nov          110           91.776

Dec          115           95.421

October forecast is 84.72

Diff: 2   Page Ref: 697

Keywords: simple exponential smoothing, exponential smoothing

AACSB: Analytic skills

59) Using a 3-month moving average, how many check-ins can be forecasted for January?

Diff: 1   Page Ref: 694

Keywords: moving averages

AACSB: Analytic skills

60) Using the exponential smoothing factor 0.3, how many check-ins can be forecasted for January? Assume the forecast for December was 122 rooms.

Diff: 3   Page Ref: 697

Keywords: exponential smoothing

AACSB: Analytic skills

61) The following data summarizes the historical demand for a product.

 Month Actual Demand March 20 April 25 May 40 June 35 July 30 August 45

Use exponential smoothing with α = .2 and a smoothed forecast for July of 32 to determine August and September’s smoothed forecasts.

Answer: FAugust = 31.6, FSeptember = 34.28

Diff: 2   Page Ref: 697

Keywords: simple exponential smoothing

AACSB: Analytic skills

62) If the forecast is 33 and the actual value is 44, then the error this period is ________.

Diff: 1   Page Ref: 706

Keywords: forecast accuracy

AACSB: Analytic skills

63) If the forecast is 25 and the actual value is 25, then the error this period is ________.

Diff: 1   Page Ref: 706

Keywords: forecast accuracy

AACSB: Analytic skills

64) The following sales data are available for 2003-2008:

Determine a 4-year moving average forecast for 2008 and 2009.

Answer: F2008 = 15.5, F2009 = 18.75

Diff: 2   Page Ref: 694

Keywords: moving average method

AACSB: Analytic skills

65) The following sales data are available for 2003-2008:

 Year Sales Forecast 2003 7 9 2004 12 10 2005 14 15 2006 20 22 2007 16 18 2008 25 21

Calculate the average error.

Diff: 2   Page Ref: 707

Keywords: moving average method

AACSB: Analytic skills

66) If the forecast is 14 and the actual value is 15, then the error this period is

Diff: 1   Page Ref: 706

Keywords: forecast accuracy

AACSB: Analytic skills

67) If the absolute errors were calculated for 5 periods and the sum of the absolute deviation is 60, what is the value of the MAD?

Diff: 2   Page Ref: 707

Keywords: Mean Absolute Deviation

AACSB: Analytic skills

68) Assume that the forecasted demand for 2006 is 15. Use the following data set and exponential smoothing with α = 0.4 and determine the forecasted demand for 2009.

Answer: F2007 = 15.4, F2008 = 17.24, F2009 = 17.544

Diff: 2   Page Ref: 698

Keywords: simple exponential smoothing

AACSB: Analytic skills

69) Given the following data, compute the MAD for the forecast.

Year     Demand           Forecast

 2001 16 18 2002 20 19 2003 18 24

Diff: 2   Page Ref: 707

Keywords: simple exponential smoothing, forecast error, forecast accuracy

AACSB: Analytic skills

70) The following sales data are available for 2003-2008.

Determine a 4-year weighted moving average forecast for 2009, where weights are

W1 = .1, W2 = .2, W3 = .2 and W4 = .5.

Diff: 2   Page Ref: 696

Keywords: weighted moving average

AACSB: Analytic skills

71) Quarterly sales is given for the past 3 years. Determine the seasonal factors for each quarter.

 Winter Spring Summer Fall Year 1 4800 4500 4100 5500 Year 2 5700 3800 4500 6000 Year 3 6000 4600 4900 6500

Answer: Swinter = .27, Sspring = .2118, Ssummer = .2217, Sfall = .2956

Diff: 2   Page Ref: 704

Keywords: seasonal factors

AACSB: Analytic skills

Recent past demand for product ZXT is given in the following table.

 Month Actual Demand February 20 March 22 April 33 May 35 June 31 July 48 August 41

72) Determine the forecasted demand for April and May based on adjusted exponential smoothing with α = .2, β = .3, a February forecast of 20, and T=0.

Diff: 3   Page Ref: 700

AACSB: Analytic skills

73) Base on a three-month weighted moving average with weights w1 = .1, w2 = .4, and w3 = .5 (most recent), determine the forecasted demand for August and September. What is the forecast error in August?

Answer: FAugust = 39.9, FSeptember = 42.8, eAugust = 1.1

Diff: 2   Page Ref: 706

Keywords: moving avg method, weighted moving avg method, forecast error

AACSB: Analytic skills

74) Use simple exponential smoothing with alpha = .4 and determine the forecasted demand for August and September. Assume that the smoothed forecast for July is 38.

Answer: FAugust = 42, FSeptember = 41.6

Diff: 2   Page Ref: 697

Keywords: simple exponential smoothing

AACSB: Analytic skills

75) Simple exponential smoothing is being used to forecast demand. The previous forecast of 66 turned out to be four units less than actual demand. If the next forecast is 66.6, what is the value of the smoothing constant, α?

Diff: 2   Page Ref: 697

Keywords: exponential smoothing

AACSB: Analytic skills

76) Robert wants to know if there is a relation between money spent on gambling and winnings.

What is the coefficient of determination?

Diff: 3   Page Ref: 716

Keywords: regression models, coefficient of determination

AACSB: Analytic skills

Robert has the following accounts on money spent on gambling and winnings:

77) Develop a regression equation that relates the money Robert spends and the money he wins.

Answer: Y = 2613.3 + 0.8383 X, where Y = money won

Diff: 3   Page Ref: 714

Keywords: linear regression models, regression analysis

AACSB: Analytic skills

78) Determine the correlation coefficient and the coefficient of determination.

Answer: r2 =.835 and r = .913

Diff: 3   Page Ref: 716

Keywords: linear regression models, regression analysis

AACSB: Analytic skills

Sally has been running the following number of ads in the local newspaper to help attract customers into her store. She has also been keeping track of customers who have come into the store as a result of the ads, as well as the amount of money they spend.

This is the data from the last 4 weeks:

79) Determine the equation that relates ads and increased sales.

Answer: Y = 50 + 18X

Diff: 3   Page Ref: 715

Keywords: regression analysis, linear regression models

AACSB: Analytic skills

80) If Sally runs 15 ads, how much will sales increase?

Answer: Y = 50 + 18(15) = 320

Diff: 3   Page Ref: 715

Keywords: regression analysis, linear regression models

AACSB: Analytic skills

81) If Sally runs 10 ads, how much will sales increase?

Answer:annot say, because 10 it outside the range of values for the independent variable. However, a student using the regression equation may suggest that a sales increase of \$230 is reasonable.

Diff: 3   Page Ref: 706

Keywords: regression analysis, linear regression models

AACSB: Analytic skills

Consider the following annual sales data for 2001-2008:

 Year Sales 2001 2 2002 4 2003 10 2004 8 2005 14 2006 18 2007 17 2008 20

82) Use the linear regression method and determine the estimated sales equation.

Answer: Y = -.2143 + 2.6309 X. This equation is appropriate if years are treated as 1, 2, 3, etc.

Y = -5262.12 + 2.6309 X. This equation is appropriate if years are treated as 2001, 2002, 2003, etc.

Diff: 2   Page Ref: 716

Keywords: regression analysis, linear regression method

AACSB: Analytic skills

83) Calculate the coefficient of determination.

Diff: 2   Page Ref: 716

Keywords: correlation coefficient and the coefficient of determination

AACSB: Analytic skills

84) Calculate the correlation coefficient.

Diff: 2   Page Ref: 716

Keywords: correlation coefficient and the coefficient of determination

AACSB: Analytic skills

A rendering plant wishes to use the data (sales records from a few local businesses and the month of the year) to help determine their supply level for the coming months. The records shown in the table provide an excellent opportunity for you to assist them with their forecasting.

 Month Sales Pounds January 45 54.3 February 57 63.8 March 32 39.5 April 44 49.8 May 51 52.3 June 34 39.9

85) What is the regression equation resulting from using Sales to forecast Pounds?

Answer: Pounds = 9.52 + 0.922 ∗ Sales

Diff: 2   Page Ref: 713

Keywords: regression methods

AACSB: Analytic skills

86) What is the regression equation resulting from using the month, where January=1, February=2, etc.) to forecast Pounds?

Answer: Pounds = 59.55 -2.74 ∗ Month

Diff: 2   Page Ref: 713

Keywords: regression methods

AACSB: Analytic skills

87) What is the regression equation resulting from using both the month (where January=1, February=2, etc.) and the level of Sales to forecast Pounds?

Answer: Pounds = 17.76 + 0.84 ∗ Sales – 1.29 ∗ Month

Diff: 2   Page Ref: 719

Keywords: multiple linear regression analysis

AACSB: Analytic skills

88) What are the salient performance statistics for the simple regression of Pounds on Sales? Provide an interpretation.

Answer: The coefficient of determination for this equation is 0.922, which means that 92% of the variation in Pounds can be explained by the value of the independent variable Sales. The correlation between the two variables is 0.96, which is virtually a straight line.

Diff: 2   Page Ref: 713

Keywords: regression methods

AACSB: Analytic skills

89) What are the salient performance statistics for the simple regression model that predicts the level of Pounds by the number of the month the company is in (with January=1)? Provide an interpretation.

Answer: The coefficient of determination is 0.31, meaning that knowledge of the month can determine about 31% of the variation in the Pounds variable. The correlation coefficient between the two variables is -0.55, so as the month number increases, the level of Pounds decreases.

Diff: 2   Page Ref: 713

Keywords: regression methods

AACSB: Analytic skills

The following data summarizes the historical demand for a product:

 Month Actual Demand March 20 April 25 May 40 June 35 July 30 August 45

90) Use a four-period moving average to determine the forecasted demand for July, August, and September.

Answer: July forecast = 30; August forecast = 32.5; September forecast = 37.5

Diff: 2   Page Ref: 694

Keywords: moving avg method, forecast accuracy/error, MAPD, MAD, MSE

AACSB: Analytic skills

91) If the forecasted demand for June, July, and August is 32, 38 and 42, respectively, what is MAD?

Diff: 2   Page Ref: 706

Keywords: moving avg method, forecast accuracy/error, MAPD, MAD, MSE

AACSB: Analytic skills

92) If the forecasted demand for June, July, and August is 32, 38 and 42, respectively, what is MSE?

Diff: 2   Page Ref: 708

Keywords: moving avg method, forecast accuracy/error, MAPD, MAD, MSE

AACSB: Analytic skills

93) If the forecasted demand for June, July, and August is 32, 38 and 42, respectively, what is MAPD?

Answer: MAPD = .127 or 12.7%

Diff: 2   Page Ref: 707

Keywords: moving avg method, forecast accuracy/error, MAPD, MAD, MSE

AACSB: Analytic skills

94) A manager uses the following equation to predict monthly receipts: Yt = 4,000 + 30t. What is the forecast for July of next year if t = 0 in April of this year?

Answer: t = 15, so Yt = 4450

Diff: 2   Page Ref: 716

Keywords: regression analysis

AACSB: Analytic skills

95) A local gym has discovered that their demand for personal trainers (measured in hours) is related not only to their own advertising expenditures in the prior month, but also to the demand for doughnuts and swim gear in the prior month at neighboring stores. The gym has developed the following regression model to forecast demand for personal trainers:

Demand = 185 + (0.15∗advertising expenditures) – (0.05∗doughnuts) + (0.23∗swim gear sales)

What is the forecast for October, given advertising expenditures of 1000, doughnut sales of 2450, and swim gear sales of 782 in September?

Diff: 2   Page Ref: 712

Section Heading: Time Series Forecasting Using Excel

Keywords: multiple linear regression analysis

AACSB: Analytic skills

96) A ________ is a gradual, long-term, up-or-down movement of demand.

1. A) seasonal pattern
2. B) cycle
3. C) trend
4. D) prediction

Diff: 1   Page Ref: 690

Keywords: trend, forecasting components

97) A ________ is an up-and-down repetitive movement that repeats itself over a time span of more than 1 year.

1. A) prediction
2. B) seasonal pattern
3. C) trend
4. D) cyclical pattern

Diff: 1   Page Ref: 690

Keywords: seasonal pattern

98) ________ methods are the most common type of forecasting method for the long-term strategic planning process.

1. A) Regression
2. B) Qualitative
3. C) Time series
4. D) Queuing

Diff: 2   Page Ref: 691

Keywords: qualitative methods

99) ________ is a category of statistical techniques that uses historical data to predict future behavior.

1. A) Qualitative methods
2. B) Regression
3. C) Time series
4. D) Quantitative methods

Diff: 2   Page Ref: 691

Keywords: time series analysis

100) ________ use management judgment, expertise, and opinion to make forecasts.

1. A) Qualitative methods
2. B) Regression
3. C) Time series
4. D) Quantitative methods

Diff: 2   Page Ref: 691

Keywords: qualitative methods

101) The ________ is a procedure for developing a consensus forecast about what will occur in the future.

1. A) Delphi method
2. B) quantitative method
3. C) regression equation
4. D) time series forecasting method

Diff: 3   Page Ref: 693

Keywords: Delphi method

102) ________ has become increasingly crucial to compete in the modern international business environment.

1. A) The Delphi method
2. B) Technological forecasting
3. C) Prediction
4. D) Exponential smoothing

Diff: 2   Page Ref: 693

Keywords: technological forecasting

103) Consider the following graph of sales.

Which of the following characteristics is exhibited by the data?

1. A) trend only
2. B) trend plus seasonal
3. C) trend plus random
4. D) none of the above

Diff: 2   Page Ref: 691

Keywords: forecasting components, trend, cyclical, seasonal

104) Consider the following graph of sales.

Which of the following characteristics is exhibited by the data?

1. A) trend only
2. B) trend plus seasonal
3. C) trend plus random
4. D) seasonal only

Diff: 2   Page Ref: 691

Keywords: forecasting components, trend, random, seasonal

105) Consider the following graph of sales.

Which of the following characteristics is exhibited by the data?

1. A) trend only
2. B) trend plus seasonal
3. C) trend plus irregular
4. D) seasonal

Diff: 2   Page Ref: 691

Keywords: forecasting components, trend, seasonal, irregular

106) ________ moving averages react more slowly to recent demand changes than do ________ moving averages.

1. A) Longer-period, shorter-period
2. B) Shorter-period, longer-period
3. C) Longer-period, longer-period
4. D) Shorter-period, shorter-period

Diff: 2   Page Ref: 695

Keywords: moving averages, time series analysis

107) ________ are good for stable demand with no pronounced behavioral patterns.

1. A) Longer-period moving averages
2. B) Shorter-period moving averages
3. C) Moving averages
4. D) Weighted moving averages

Diff: 2   Page Ref: 693

Keywords: moving averages, time series analysis

108) ________ methods assume that what has occurred in the past will continue to occur in the future.

1. A) Time series
2. B) Regression
3. C) Quantitative
4. D) Qualitative

Diff: 2   Page Ref: 693

Keywords: time series analysis

109) In exponential smoothing, the closer alpha is to ________, the greater the reaction to the most recent demand.

1. A) -1
2. B) 0
3. C) 1
4. D) -1 or 1

Diff: 2   Page Ref: 697

Keywords: exponential smoothing

110) In adjusted exponential smoothing, the closer beta is to ________, the stronger a trend is reflected.

1. A) -1 or 1
2. B) -1
3. C) 0
4. D) 1

Diff: 2   Page Ref: 700

111) ________ is a linear regression model relating demand to time.

1. A) Linear trend
2. B) Linear regression
3. C) Forecast demand
4. D) Linear equation

Diff: 2   Page Ref: 703

Keywords: linear regression model, regression analysis

112) Which of the following possible values of alpha would cause exponential smoothing to respond the most slowly to sudden changes in forecast errors?

1. A) .01
2. B) .50
3. C) .90
4. D) 3.14

Diff: 2   Page Ref: 697

Keywords: simple exponential smoothing

113) Given an actual demand of 59, a previous forecast of 64, and an alpha of .3, what would the forecast for the next period be using simple exponential smoothing?

1. A) 36.9
2. B) 57.5
3. C) 60.5
4. D) 62.5

Diff: 2   Page Ref: 697

Keywords: simple exponential smoothing

AACSB: Analytic skills

114) ________ is the difference between the forecast and actual demand.

1. A) Forecast mistake
2. B) Forecast error
4. D) Forecast accuracy

Diff: 2   Page Ref: 705

Keywords: forecast error, forecast accuracy

115) ________ is absolute error as a percentage of demand.

1. A) Cumulative error
3. C) MAPD
4. D) Average error

Diff: 3   Page Ref: 707

Keywords: MAPD, forecast accuracy

116) ________ indicates a forecast is biased high.

1. A) Large +
2. B) Large –
3. C) Large :
4. D) Large x

Diff: 2   Page Ref: 706

Keywords: cumulative error, average error

AACSB: Analytic skills

117) ________ is a measure of the strength of the relationship between independent variable(s) and a dependent variable.

1. A) Correlation
2. B) Linear regression
3. C) Coefficient of determination
4. D) Regression

Diff: 2   Page Ref: 715

Keywords: correlation, regression methods, linear regression model

118) ________ is the percentage of the variation in the dependent variable that results from the independent variable.

1. A) Regression
2. B) Coefficient of determination
3. C) Correlation
4. D) Linear regression

Diff: 2   Page Ref: 716

Keywords: coefficient of determination, reg methods, linear reg model

119) Coefficient of determination is the percentage of the variation in the ________ variable that results from the ________ variable.

1. A) dependent, dependent
2. B) independent, dependent
3. C) dependent, independent
4. D) independent, independent

Diff: 3   Page Ref: 716

Keywords: coefficient of determination, linear reg model, reg methods

120) Consider the following demand and forecast.

 Period Demand Forecast 1 7 10 2 12 15 3 18 20 4 22

If MAD = 2 for the four periods under consideration, what is the forecast for period 4?

1. A) 19
2. B) 20
3. C) 21
4. D) 22

Diff: 2   Page Ref: 699

AACSB: Analytic skills

Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame:

121) Use a 2-period moving average to forecast demand for period 7.

1. A) 227.5
2. B) 275
3. C) 280
4. D) 290

Diff: 2   Page Ref: 686

Keywords: moving average method

AACSB: Analytic skills

122) Use a 3-period moving average to forecast demand for period 7.

1. A) 283.33
2. B) 280
3. C) 290
4. D) 310

Diff: 2   Page Ref: 686

Keywords: moving average method

AACSB: Analytic skills

123) If the forecast for period 5 is equal to 275, use exponential smoothing to compute a forecast for period 7 if α = .40.

1. A) 273
2. B) 277
3. C) 267.8
4. D) 286.2

Diff: 2   Page Ref: 689

Keywords: exponential smoothing

AACSB: Analytic skills

The following data represents quarterly sales of lawnmowers.

 Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 1 150 140 190 165 2 160 148 210 175

124) What is the seasonal index for the third quarter? (Round to the nearest hundredth.)

1. A) .20
2. B) .22
3. C) .26
4. D) .30

Diff: 2   Page Ref: 697-698

Keywords: seasonal factors

AACSB: Analytic skills

125) What is the seasonal index for the fourth quarter? (Round to the nearest hundredth.)

1. A) .20
2. B) .23
3. C) .25
4. D) .30

Diff: 2   Page Ref: 697-698

Keywords: seasonal factors

AACSB: Analytic skills

126) The manager of “Skis 4 U” is preparing a forecast for February of 2010. Demand exhibits both trend and seasonality. The trend equation for monthly demand is y = 4375 + 80t, where t = 1 for January 2009. The seasonal index for February is 1.25. The forecast for February is:

1. A) 4575
2. B) 4583
3. C) 5668
4. D) 6769

Diff: 2   Page Ref: 697-698

Keywords: seasonal factors

AACSB: Analytic skills

127) Given forecast errors of 6, 4, 0 and -2, what is the mean absolute deviation?

1. A) 2
2. B) 3
3. C) 4
4. D) 2.67
5. E) none of the above

Diff: 2   Page Ref: 699

128) Given forecast errors of 6, 4, 0 and -2, what is the mean squared error?

1. A) 14
2. B) 18.67
3. C) 16
4. D) 12
5. E) none of the above

Diff: 2   Page Ref: 698

Keywords: forecast error, MSE

AACSB: Analytic skills

A rendering plant wishes to use the data (sales records from a few local businesses and the month of the year) to help determine their supply level for the coming months. The records shown in the table provide an excellent opportunity for you to assist them with their forecasting.

 Month Sales Pounds January 45 54.3 February 57 63.8 March 32 39.5 April 44 49.8 May 51 52.3 June 34 39.9

129) What is a three-period moving average forecast for the month of July?

1. A) 47.33
2. B) 46.10
3. C) 45.38
4. D) 44.29

Diff: 2   Page Ref: 694

Keywords: moving averages

AACSB: Analytic skills

130) What is the three-period weighted moving average for July using the weights 0.5 (most recent), 0.3, and 0.2?

1. A) 48.99
2. B) 45.6
3. C) 49.51
4. D) 46.09

Diff: 2   Page Ref: 696

Keywords: weighted moving average method

AACSB: Analytic skills

131) Using 1 to represent January, 2 to represent February, and so on, what is the intercept for the regression equation that predicts the pounds of supplies available?

1. A) 0.55
2. B) -2.74
3. C) 59.55
4. D) 8.87

Diff: 2   Page Ref: 716-719

Keywords: regression analysis

AACSB: Analytic skills

132) What is the forecast for July if exponential smoothing with an alpha=.04 generated a forecast of 43.0 for June?

1. A) 41.25
2. B) 40.64
3. C) 43.16
4. D) 42.88

Diff: 2   Page Ref: 697

Keywords: exponential smoothing

AACSB: Analytic skills

133) What is the slope of the regression equation developed when the Sales data are used to predict the Pounds?

1. A) 0.92
2. B) 0.86
3. C) 0.80
4. D) 0.71

Diff: 2   Page Ref: 715

Keywords: linear regression

AACSB: Analytic skills

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Mat 540 Week 2 Homework Problems – Chapter 1 and Chapter 11

Complete the following problems from Chapter 1:

Problems 2, 4, 12, 14, 20, 22

Complete the following problems from Chapter 11:

Problems 18, 20, 26, 28, 30

Chapter 1:

2) The Retread Tire Company recaps tires. The fixed annual cost of the recapping operation is

\$60,000. The variable cost of recapping a tire is \$9. The company charges \$25 to recap a tire.

1. For an annual volume of 12,000 tires, determine the total cost, total revenue, and profit.
2. Determine the annual break-even volume for the Retread Tire Company operation.

4) Evergreen Fertilizer Company produces fertilizer. The company’s fixed monthly cost is \$25,000, and its variable cost per pound of fertilizer is \$0.15. Evergreen sells the fertilizer for \$0.40 per pound. Determine the monthly break-even volume for the company.

12) If Evergreen Fertilizer Company in Problem 4 changes the price of its fertilizer from \$0.40 per pound to \$0.60 per pound, what effect will the change have on the break-even volume?

14) If Evergreen Fertilizer Company increases its advertising expenditures by \$14,000 per year, what effect will the increase have on the break-even volume computed in Problem 13?

20) Annie McCoy, a student at Tech, plans to open a hot dog stand inside Tech’s football stadium during home games. There are seven home games scheduled for the upcoming season. She must pay the Tech athletic department a vendor’s fee of \$3,000 for the season. Her stand and other equipment will cost her \$4,500 for the season. She estimates that each hot dog she sells will cost her \$0.35. She has talked to friends at other universities who sell hot dogs at games. Based on their information and the athletic department’s forecast that each game will sell out, she anticipates that she will sell approximately 2,000 hot dogs during each game.

1. What price should she charge for a hot dog in order to break even?
2. What factors might occur during the season that would alter the volume sold and thus the

break-even price Annie might charge?

1. What price would you suggest that Annie charge for a hot dog to provide her with a

reasonable profit while remaining competitive with other food vendors?

22) The College of Business at Tech is planning to begin an online MBA program. The initial start-up cost for computing equipment, facilities, course development, and staff recruitment and development is \$350,000. The college plans to charge tuition of \$18,000 per student per year. However, the university administration will charge the college \$12,000 per student for the first 100 students enrolled each year for administrative costs and its share of the tuition payments.

1. How many students does the college need to enroll in the first year to break even?
2. If the college can enroll 75 students the first year, how much profit will it make?
3. The college believes it can increase tuition to \$24,000, but doing so would reduce enrollment to 35. Should the college consider doing this?

Chapter 11

18) The following probabilities for grades in management science have been determined based on past records:

A                     .10

B                     .30

C                     .40

D                     .10

F                     .10

1.00

The grades are assigned on a 4.0 scale, where an A is a 4.0, a B a 3.0, and so on. Determine the expected grade and variance for the course.

20) An investment firm is considering two alternative investments, A and B, under possible future sets of economic conditions, good and poor. There is a .60 probability of good economic conditions occurring and a .40 probability of poor economic conditions occurring. The expected gains and losses under each economic type of conditions are shown in the following table:

 Economic Conditions Investment Good Poor A \$900,000 -\$800,000 B 120,000 70,000

Using the expected value of each investment alternative, determine which should be selected.

26) The weight of bags of fertilizer is normally distributed, with a mean of 50 pounds and a standard deviation of 6 pounds. What is the probability that a bag of fertilizer will weigh between 45 and 55 pounds.

28) The polo Development Firm is building a shopping center. It has informed renters that their rental space will be ready for occupancy in 19 months. If the expected time until the shopping center is completed is estimated to be 14 months with a standard deviation of 4 months, what is the probability that the renters will not be able to occupy in 19 months?

30) The manager of the local national Video Store sells videocassette recorders at discount prices. If the store does not have a video recorder in stock when a customer wants to buy one, it will lose the sale because the customer will purchase a recorder from one of the many local competitors. The problem is that the cost of renting warehouse space to keep enough recorders in inventory to meet all demand is excessively high. The manager has determined that if 90% of customers demand for recorders can be met, then the combined cost of lost sales and inventory will be minimized. The manager has estimated that monthly demand for recorders is normally distributed, with a mean of 180 recorders and a standard deviation of 60. Determine the number of recorders the manager should order each month to meet 92% of customer demand.

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Mat 540 Problems Chapter 12 Homework

Complete the following problems from Chapter 12:

• Problems 8, 16, 24, 32, 36

Refer to the tree diagram below to complete problem 36:

See email for diagram.

8) A local real estate investor in Orlando is considering three alternative investments: a model, a restaurant, or a theater. Profits from the motel or restaurant will be affected by the availability of gasoline and the number of tourists; profits from the theater will be relatively stable under any conditions. The following payoff table shows the profit or loss that could result from each investment:

 Gasoline Availability Investment Shortage Stable Supply Surplus Morel \$-8,000 \$15,000 \$20,000 Restaurant 2,000 8,000 6,000 Theater 6,000 6,000 5,000

Determine the best investment, using the following decision criteria:

1. Maximax
2. Maximin
3. Minimax regret
4. Hurwicz (α = .4)
5. Equal likelihood

16) A concession manager at the Tech versus A&M football game must decide whether to have the vendors sell sun visors or umbrellas. There is a 30% chance of rain, a 15% chance of overcast skies, and a 55% chance of sunshine, according to the weather forecast in College Junction, where the game is to be held. The manager estimates that the following profits will result from each decision, given each set of weather conditions;

 Weather Conditions Decision Rain .30 Overcast .15 Sunshine .55 Sun visors \$-500 \$-200 \$1,500 Umbrellas 2,000 0 -900

1. Compute the expected value for each decision and select the best one.
2. Develop the opportunity loss table and compute the expected opportunity loss for each decision.

24) In problem 13 the Place-Plus real estate development firm has hired an economist to assign a probability for each direction interest rates may take over the next 5 years. The economist has determined that there is a .50 probability that interest rates will decline during the next 5 years is .40, the probability that rates will remain stable, and a .10 probability that rates will increase.

1. Using the expected value, determine the best project.
2. Determine the expected value of perfect information.

32) The director of career advising at Orange Community College wants to use decision analysis to provide information to help students decide which 2-year degree program they should pursue. The director has set up the following payoff table for six of the most popular and success degree programs at OCC that shows the estimated 5-year gross income (\$) from each degree for four future economic conditions:

 Economic Conditions Degree Program Recession Average Good Robust Graphic design 145,000 175,000 220,000 260,000 Nursing 150,000 180,000 205,000 215,000 Real estate 115,000 165,000 220,000 320,000 Medical Technology 130,000 180,000 210,000 280,000 Culinary Technology 115,000 145,000 235,000 305,000 Computer Information Technology 125,000 150,000 190,000 250,000

36) Construct a decision tree for the decision situation described in Problem 25 and indicate the best decision.

25) Fenton and Farrah Friendly, husband-and-wife car dealers, are soon going to open a new dealership. They have three offers from a foreign compact car company, from a U.S.-producer of full-sized cars, and from a truck company. The success of each type of dealership will depend on how much gasoline is going to be available during the next few years. The profit from each type of dealership, given the availability of gas, is shown in the following payoff table:

 Gasoline Availability Dealership Shortage .6 Surplus .4 Compact cars \$300,000 \$150,000 Full-sized cars -100,000 600,00 Trucks 120,000 170,000

Determine which type of dealership the couple should purchase.

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MAT 540 Chapter 14 Homework Problems

1. The Hoylake Rescue Squad receives an emergency call every 1, 2, 3, 4, 5, or 6 hours, according to the following probability distribution. The squad is on duty 24 hours per day, 7 days per week:

Time Between Emergency Calls (hr.)

Probability

1 .05 2 .10 3 .30 4 .30 5 .20 6 .05

1.00

1. Simulatetheemergencycallsfor3days(notethatthiswillrequirea“running,”or cumulative, hourly clock), using the random number table.
2. Computetheaveragetimebetweencallsandcomparethisvaluewiththeexpected value of the time between calls from the probability distribution. Why are the results different?
3. Howmanycallsweremadeduringthe3-dayperiod?Canyoulogicallyassumethatthisis an average number of calls per 3-day period? If not, how could you simulate to determine such an average?

1. The time between arrivals of cars at the Petroco Service Station is defined by the following proba- bility distribution:

Time Between Arrivals (min.)

Probability

1 .15 2 .30 3 .40 4 .15

1.00

1. Simulatethearrivalofcarsattheservicestationfor20arrivalsandcomputetheaverage time between arrivals.
2. Simulatethearrivalofcarsattheservicestationfor1hour,usingadifferentstreamof random numbers from those used in (a) and compute the average time between arrivals.
3. Comparetheresultsobtainedin(a)and(b).

1. The Dynaco Manufacturing Company produces a product in a process consisting of operations of five machines. The probability distribution of the number of machines that will break down in a week follows:

0 .10 1 .10 2 .20 3 .25 4 .30 5 .05

1.00

1. Simulatethemachinebreakdownsperweekfor20weeks.
2. Compute the average number of machines that will break down per week.

1. Simulate the decision situation described in Problem 16(a) at the end of Chapter 12 for 20 weeks, and recommend the best decision.

1. Every time a machine breaks down at the Dynaco Manufacturing Company (Problem 3), either 1, 2, or 3 hours are required to fix it, according to the following probability distribution:

Repair Time (hr.)

Probability

1 .30 2 .50 3 .20

1.00

1. Simulate the repair time for 20 weeks and then compute the average weekly repair time.

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MAT 540 Homework Chapter 15 Problems

MAT 540 Homework Problems Week 4 Chapter 15

Chapter 15

1.   The manager of the Carpet City outlet needs to make an accurate forecast of the demand for Soft Shag carpet (its biggest seller).  If the manager does not order enough carpet from the carpet mill, customers will buy their carpet from one of Carpet City’s many competitors. The manager has collected the following demand data for the past 8 months:
 Month Demand for Soft Shag Carpet (1,000 yd.) 1 8 2 12 3 7 4 9 5 15 6 11 7 10 8 12

1. Compute a 3-month moving average forecast for months 4 through 9.
2. Compute a weighted 3-month moving average forecast for months 4 through 9. Assign weights of 0.55, 0.33, and 0.12 to the months in sequence, starting with the most recent month.
3. Compare the two forecasts by using MAD.  Which forecast appears to be more accurate?
1.   The manager of the Petroco Service Station wants to forecast the demand for unleaded gasoline next month so that the proper number of gallons can be ordered from the distributor. The owner has accumulated the following data on demand for unleaded gasoline from sales during the past 10 months:
 Month Gasoline Demanded (gal.) October 800 November 725 December 630 January 500 February 645 March 690 April 730 May 810 June 1,200 July 980

1. Compute an exponentially smoothed forecast, using an α value of 0.30.
2. Compute the MAPD.
1.   Emily Andrews has invested in a science and technology mutual fund.  Now she is considering liquidating and investing in another fund.  She would like to forecast the price of the science and technology fund for the next month before making a decision.  She has collected the following data on the average price of the fund during the past 20 months:
 Month Fund Price 1 \$63 1/4 2 60 1/8 3 61 3/4 4 64 1/4 5 59 3/8 6 57 7/8 7 62 1/4 8 65 1/8 9 68 1/4 10 65 1/2 11 68 1/8 12 63 1/4 13 64 3/8 14 68 5/8 15 70 1/8 16 72 3/4 17 74 1/8 18 71 3/4 19 75 1/2 20 76 3/4

1. Using a 3-month average, forecast the fund price for month 21.
2. Using a 3-month weighted average with the most recent month weighted 0.60, the next most recent month weighted 0.30, and the third month weighted 0.10, forecast the fund price for month 21.
3. Compute an exponentially smoothed forecast, using α=0 .40, and forecast the fund price for month 21.
4. Compare the forecasts in (a), (b), and (c), using MAD, and indicate the most accurate.

1.       Carpet City wants to develop a means to forecast its carpet sales. The store manager believes that the store’s sales are directly related to the number of new housing starts in town. The manager has gathered data from county records on monthly house construction permits and from store records on monthly sales. These data are as follows:
 Monthly Carpet Sales (1,000 yd.) Monthly Construction Permits 5 21 10 35 4 10 3 12 8 16 2 9 12 41 11 15 9 18 14 26

1. Develop a linear regression model for these data and forecast carpet sales if 30 construction permits for new homes are filed.
2. Determine the strength of the causal relationship between monthly sales and new home construction by using correlation.
1.       The manager of Gilley’s Ice Cream Parlor needs an accurate forecast of the demand for ice cream. The store orders ice cream from a distributor a week ahead; if the store orders too little, it loses business, and if it orders too much, the extra must be thrown away. The manager believes that a major determinant of ice cream sales is temperature (i.e., the hotter the weather, the more ice cream people buy). Using an almanac, the manager has determined the average daytime temperature for 10 weeks, selected at random, and from store records he has determined the ice cream consumption for the same 10 weeks. These data are summarized as follows:
 Week Average Temperature (degrees) Ice Cream Sold (gal.) 1 73 110 2 65 95 3 81 135 4 90 160 5 75 97 6 77 105 7 82 120 8 93 175 9 86 140 10 79 121

1. Develop a linear regression model for these data and forecast the ice cream consumption if the average weekly daytime temperature is expected to be 85 degrees.
2. Determine the strength of the linear relationship between temperature and ice cream consumption by using correlation.
1. Compute the coefficient of determination for the data in Problem 27 and explain its meaning.

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MAT 540 Homework Chapter 15 Problems

MAT 540 Homework Problems Week 4 Chapter 15

Chapter 15

The manager of the Carpet City outlet needs to make an accurate forecast of the demand for Soft Shag carpet (its biggest seller). If the manager does not order enough carpet from the carpet mill, customers will buy their carpet from one of Carpet City’s many competitors. The manager has collected the following demand data for the past 8 months:
Month Demand for Soft Shag Carpet (1,000 yd.)
1 8
2 12
3 7
4 9
5 15
6 11
7 10
8 12

Compute a 3-month moving average forecast for months 4 through 9.
Compute a weighted 3-month moving average forecast for months 4 through 9. Assign weights of 0.55, 0.33, and 0.12 to the months in sequence, starting with the most recent month.
Compare the two forecasts by using MAD. Which forecast appears to be more accurate?
The manager of the Petroco Service Station wants to forecast the demand for unleaded gasoline next month so that the proper number of gallons can be ordered from the distributor. The owner has accumulated the following data on demand for unleaded gasoline from sales during the past 10 months:
Month Gasoline Demanded (gal.)
October 800
November 725
December 630
January 500
February 645
March 690
April 730
May 810
June 1,200
July 980

Compute an exponentially smoothed forecast, using an α value of 0.30.
Compute the MAPD.
Emily Andrews has invested in a science and technology mutual fund. Now she is considering liquidating and investing in another fund. She would like to forecast the price of the science and technology fund for the next month before making a decision. She has collected the following data on the average price of the fund during the past 20 months:
Month Fund Price
1 \$63 1/4
2 60 1/8
3 61 3/4
4 64 1/4
5 59 3/8
6 57 7/8
7 62 1/4
8 65 1/8
9 68 1/4
10 65 1/2
11 68 1/8
12 63 1/4
13 64 3/8
14 68 5/8
15 70 1/8
16 72 3/4
17 74 1/8
18 71 3/4
19 75 1/2
20 76 3/4

Using a 3-month average, forecast the fund price for month 21.
Using a 3-month weighted average with the most recent month weighted 0.60, the next most recent month weighted 0.30, and the third month weighted 0.10, forecast the fund price for month 21.
Compute an exponentially smoothed forecast, using α=0 .40, and forecast the fund price for month 21.
Compare the forecasts in (a), (b), and (c), using MAD, and indicate the most accurate.

Carpet City wants to develop a means to forecast its carpet sales. The store manager believes that the store’s sales are directly related to the number of new housing starts in town. The manager has gathered data from county records on monthly house construction permits and from store records on monthly sales. These data are as follows:
Monthly Carpet Sales (1,000 yd.) Monthly Construction Permits
5 21
10 35
4 10
3 12
8 16
2 9
12 41
11 15
9 18
14 26

Develop a linear regression model for these data and forecast carpet sales if 30 construction permits for new homes are filed.
Determine the strength of the causal relationship between monthly sales and new home construction by using correlation.
The manager of Gilley’s Ice Cream Parlor needs an accurate forecast of the demand for ice cream. The store orders ice cream from a distributor a week ahead; if the store orders too little, it loses business, and if it orders too much, the extra must be thrown away. The manager believes that a major determinant of ice cream sales is temperature (i.e., the hotter the weather, the more ice cream people buy). Using an almanac, the manager has determined the average daytime temperature for 10 weeks, selected at random, and from store records he has determined the ice cream consumption for the same 10 weeks. These data are summarized as follows:
Week
Average Temperature

(degrees)

Ice Cream Sold

(gal.)

1 73 110
2 65 95
3 81 135
4 90 160
5 75 97
6 77 105
7 82 120
8 93 175
9 86 140
10 79 121

Develop a linear regression model for these data and forecast the ice cream consumption if the average weekly daytime temperature is expected to be 85 degrees.
Determine the strength of the linear relationship between temperature and ice cream consumption by using correlation.
Compute the coefficient of determination for the data in Problem 27 and explain its meaning.

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MAT 540 Chapter 14 Homework Problems

The Hoylake Rescue Squad receives an emergency call every 1, 2, 3, 4, 5, or 6 hours, according to the following probability distribution. The squad is on duty 24 hours per day, 7 days per week:
Time Between Emergency Calls (hr.)

Probability

1 .05 2 .10 3 .30 4 .30 5 .20 6 .05

1.00

Simulatetheemergencycallsfor3days(notethatthiswillrequirea“running,”or cumulative, hourly clock), using the random number table.
Computetheaveragetimebetweencallsandcomparethisvaluewiththeexpected value of the time between calls from the probability distribution. Why are the results different?
Howmanycallsweremadeduringthe3-dayperiod?Canyoulogicallyassumethatthisis an average number of calls per 3-day period? If not, how could you simulate to determine such an average?

The time between arrivals of cars at the Petroco Service Station is defined by the following proba- bility distribution:
Time Between Arrivals (min.)

Probability

1 .15 2 .30 3 .40 4 .15

1.00

Simulatethearrivalofcarsattheservicestationfor20arrivalsandcomputetheaverage time between arrivals.
Simulatethearrivalofcarsattheservicestationfor1hour,usingadifferentstreamof random numbers from those used in (a) and compute the average time between arrivals.
Comparetheresultsobtainedin(a)and(b).

The Dynaco Manufacturing Company produces a product in a process consisting of operations of five machines. The probability distribution of the number of machines that will break down in a week follows:
0 .10 1 .10 2 .20 3 .25 4 .30 5 .05

1.00

Simulatethemachinebreakdownsperweekfor20weeks.
Compute the average number of machines that will break down per week.

Simulate the decision situation described in Problem 16(a) at the end of Chapter 12 for 20 weeks, and recommend the best decision.

Every time a machine breaks down at the Dynaco Manufacturing Company (Problem 3), either 1, 2, or 3 hours are required to fix it, according to the following probability distribution:
Repair Time (hr.)

Probability

1 .30 2 .50 3 .20

1.00

Simulate the repair time for 20 weeks and then compute the average weekly repair time.

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Mat 540 Problems Chapter 12 Homework

Complete the following problems from Chapter 12:

Problems 8, 16, 24, 32, 36
Refer to the tree diagram below to complete problem 36:

See email for diagram.

8) A local real estate investor in Orlando is considering three alternative investments: a model, a restaurant, or a theater. Profits from the motel or restaurant will be affected by the availability of gasoline and the number of tourists; profits from the theater will be relatively stable under any conditions. The following payoff table shows the profit or loss that could result from each investment:

Gasoline Availability
Investment Shortage Stable Supply Surplus
Morel \$-8,000 \$15,000 \$20,000
Restaurant 2,000 8,000 6,000
Theater 6,000 6,000 5,000
Determine the best investment, using the following decision criteria:

Maximax
Maximin
Minimax regret
Hurwicz (α = .4)
Equal likelihood
16) A concession manager at the Tech versus A&M football game must decide whether to have the vendors sell sun visors or umbrellas. There is a 30% chance of rain, a 15% chance of overcast skies, and a 55% chance of sunshine, according to the weather forecast in College Junction, where the game is to be held. The manager estimates that the following profits will result from each decision, given each set of weather conditions;

Weather Conditions
Decision Rain
.30 Overcast
.15 Sunshine
.55
Sun visors \$-500 \$-200 \$1,500
Umbrellas 2,000 0 -900

Compute the expected value for each decision and select the best one.
Develop the opportunity loss table and compute the expected opportunity loss for each decision.
24) In problem 13 the Place-Plus real estate development firm has hired an economist to assign a probability for each direction interest rates may take over the next 5 years. The economist has determined that there is a .50 probability that interest rates will decline during the next 5 years is .40, the probability that rates will remain stable, and a .10 probability that rates will increase.

Using the expected value, determine the best project.
Determine the expected value of perfect information.

32) The director of career advising at Orange Community College wants to use decision analysis to provide information to help students decide which 2-year degree program they should pursue. The director has set up the following payoff table for six of the most popular and success degree programs at OCC that shows the estimated 5-year gross income (\$) from each degree for four future economic conditions:

Economic Conditions
Degree Program Recession Average Good Robust
Graphic design 145,000 175,000 220,000 260,000
Nursing 150,000 180,000 205,000 215,000
Real estate 115,000 165,000 220,000 320,000
Medical Technology 130,000 180,000 210,000 280,000
Culinary Technology 115,000 145,000 235,000 305,000
Computer Information Technology 125,000 150,000 190,000 250,000

36) Construct a decision tree for the decision situation described in Problem 25 and indicate the best decision.

25) Fenton and Farrah Friendly, husband-and-wife car dealers, are soon going to open a new dealership. They have three offers from a foreign compact car company, from a U.S.-producer of full-sized cars, and from a truck company. The success of each type of dealership will depend on how much gasoline is going to be available during the next few years. The profit from each type of dealership, given the availability of gas, is shown in the following payoff table:

Gasoline Availability
Dealership
Shortage

.6

Surplus

.4

Compact cars \$300,000 \$150,000
Full-sized cars -100,000 600,00
Trucks 120,000 170,000

Determine which type of dealership the couple should purchase.