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MAT 540 Week 2 Quiz – Strayer University New
MAT/540 Week 2 Quiz 1 Chapter 1 and 11 Solution
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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.
Answer:
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.
Answer:
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
Answer:
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
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
Diff: 2 Page Ref: 12
Section Heading: Computer Solution
Keywords: spreadsheets
AACSB: Analytic skills
20) Management science techniques focus primarily on observation, model construction, and implementation to find an appropriate solution to a problem.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
30) ________ are known, constant values that are coefficients of variables in equations.
Answer:
31) ________ are pieces of information from the problem environment.
Answer:
32) A ________ is a functional relationship including variables, parameters, and equations.
Answer:
33) Management science techniques include ________ techniques, models that are represented as diagrams, presenting a pictorial representation of the system being analyzed.
Answer:
34) An increase in output typically results in an increase in the ________ cost.
Answer:
35) ________ techniques provide results that contain uncertainty, unlike mathematical programming techniques which are deterministic.
Answer:
36) ________ costs are independent of the volume of goods produced and remain constant.
Answer:
37) The difference between volume multiplied by price and the sum of fixed and variable costs is ________.
Answer:
38) ________ depend on the number of items produced.
Answer:
39) Total revenue minus total cost equals ________.
Answer:
40) The ________ is the volume that equates total revenue with total cost.
Answer:
41) A ________ represents a limitation to achieving maximum profits due to limited resources.
Answer:
42) A ________ programming technique refers to a predetermined set of mathematical steps used to solve a problem.
Answer:
43) One way to test how a management science model reacts to changes in its parameters is to conduct ________ analysis.
Answer:
44) ________ consist of models that are represented as diagrams rather than as strictly mathematical techniques.
Answer:
45) A management science technique that does not assume that all parameters are known with certainty is a(n) ________ technique.
Answer:
46) A ________ is a computer-based system that helps decision-makers address complex problems that involve different parts of an organization and operations.
Answer:
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?
Answer:
48) Researchers at John H. Stroger, Jr. Hospital of Cook County used ________ to address the problem of healthcare-associated infections in hospitals.
Answer
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
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?
Answer
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.
Answer:
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.
Answer: R(x) = 165x
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?
Answer:
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.
Answer:
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?
Answer:
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.
Answer:
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?
Answer:
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?
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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?
Answer:
69) What are some different types of decision support systems?
Answer:
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?
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
74) A model is a functional relationship that includes:
A) variables.
B) parameters.
C) equations.
D) all of the above
Answer:
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
Answer:
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
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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
Answer:
81) ________ involves determining the functional relationship between variables, parameters, and equations.
A) Problem observation
B) Problem definition
C) Model construction
D) Model solution
Answer:
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
Answer:
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.
D) access to a computer.
Answer:
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.
B) railroads.
C) politics.
D) manufacturing.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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
Answer:
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.
Answer:
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.
Answer:
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
Answer:
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.
Answer:
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.
Answer:
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
Answer:
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
Answer:
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.
Answer:
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.
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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.
Answer:
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?
Answer:
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.
Answer:
Diff: 2 Page Ref: 12
Section Heading: Computer Solution
Keywords: computer solution, spreadsheets
AACSB: Analytic skills
109) A technique that assumes certainty in its solution is referred to as
A) stochastic.
B) probabilistic.
C) deterministic.
D) parametric.
Answer:
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.
Answer:
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.
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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.
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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?
A) an Excel spreadsheet
B) an ERP
C) QM for Windows
D) OLAP
Answer:
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.
Answer:
Diff: 1 Page Ref: 503
Section Heading: Types of Probability
Keywords: deterministic techniques
2) Probabilistic techniques assume that no uncertainty exists in model parameters.
Answer:
Diff: 1 Page Ref: 503
Section Heading: Types of Probability
Keywords: probabilistic techniques
3) Objective probabilities that can be stated prior to the occurrence of an event are classical or a priori.
Answer:
Diff: 2 Page Ref: 503
Section Heading: Types of Probability
Keywords: objective probabilities, classical probabilities
4) Objective probabilities that are stated after the outcomes of an event have been observed are relative frequencies.
Answer:
Diff: 2 Page Ref: 503
Section Heading: Types of Probability
Keywords: relative frequencies
5) Relative frequency is the more widely used definition of objective probability.
Answer:
Diff: 1 Page Ref: 504
Section Heading: Types of Probability
Keywords: relative frequencies
6) Subjective probability is an estimate based on personal belief, experience, or knowledge of a situation.
Answer:
Diff: 2 Page Ref: 504
Section Heading: Types of Probability
Keywords: subjective probability
7) An experiment is an activity that results in one of several possible outcomes.
Answer:
Diff: 1 Page Ref: 505
Section Heading: Fundamentals of Probability
Keywords: experiment
8) The events in an experiment are mutually exclusive if only one can occur at a time.
Answer:
Diff: 1 Page Ref: 505
Section Heading: Fundamentals of Probability
Keywords: mutually exclusive events
9) In a given experiment, the probabilities of all mutually exclusive events sum to one.
Answer:
Diff: 1 Page Ref: 505
Section Heading: Fundamentals of Probability
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.
Answer:
Diff: 2 Page Ref: 506
Section Heading: Fundamentals of Probability
Keywords: collectively exhaustive events
11) A marginal probability is the probability of a single event occurring.
Answer:
Diff: 1 Page Ref: 506
Section Heading: Fundamentals of Probability
Keywords: marginal probability
12) A Venn diagram visually displays mutually exclusive and non-mutually exclusive events.
Answer:
Diff: 2 Page Ref: 506
Section Heading: Fundamentals of Probability
Keywords: Venn diagram
13) A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously.
Answer:
Diff: 2 Page Ref: 506
Section Heading: Fundamentals of Probability
Keywords: joint probability
14) A conditional probability is the probability that an event occurs given that another event has already occurred.
Answer:
Diff: 1 Page Ref: 508
Section Heading: Statistical Independence and Dependence
Keywords: conditional probability
15) Conditional probabilities are shown in Venn diagrams.
Answer:
Diff: 1 Page Ref: 506
Section Heading: Fundamentals of Probability
Keywords: conditional probability
16) Probability trees are used only to compute conditional probabilities.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
Diff: 1 Page Ref: 517
Section Heading: The Normal Distribution
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.
Answer:
Diff: 1 Page Ref: 519
Section Heading: The Normal Distribution
Keywords: normal distribution
AACSB: Analytic skills
21) Another name for the mean of a probability distribution is its expected value.
Answer:
Diff: 1 Page Ref: 516
Section Heading: Expected Value
Keywords: expected value
AACSB: Analytic skills
22) The expected value of a discrete random variable is greater than or equal to zero.
Answer:
Diff: 1 Page Ref: 516
Section Heading: Expected Value
Keywords: expected value
23) The variance of a discrete random variable is always greater than or equal to zero.
Answer:
Diff: 1 Page Ref: 516
Section Heading: Expected Value
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.
Answer:
Diff: 1 Page Ref: 516
Section Heading: Expected Value
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.
Answer:
Diff: 1 Page Ref: 516
Section Heading: Expected Value
Keywords: variance
AACSB: Analytic skills
26) For a typical normally distributed random variable, the standard deviation is equal to the variance.
Answer:
Diff: 1 Page Ref: 518
Section Heading: The Normal Distribution
Keywords: normal distribution
27) A normally distributed random variable has a mean of zero and a standard deviation of one.
Answer:
Diff: 1 Page Ref: 517-518
Section Heading: The Normal Distribution
Keywords: normal distribution
28) The standard normal distribution has a mean of one and a standard deviation of zero.
Answer:
Diff: 1 Page Ref: 519
Section Heading: The Normal Distribution
Keywords: standard normal distribution
29) The area under the normal curve represents probability.
Answer:
Diff: 1 Page Ref: 518
Section Heading: The Normal Distribution
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.
Answer:
Diff: 1 Page Ref: 518
Section Heading: The Normal Distribution
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.
Answer:
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.
Answer:
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 ________.
Answer: lassical or a priori
Diff: 1 Page Ref: 503
Section Heading: Types of Probability
Keywords: probabilistic techniques, objective/classical probabilities
34) ________ probability is an estimate based on a personal belief, experience, and knowledge of a situation.
Answer:
35) The events in an experiment are ________ if only one can occur at a time.
Answer:
36) The term for including all possible events that can occur in an experiment is ________.
Answer:
37) The cumulative probability for all six outcomes of tossing a fair die should end with the value ________.
Answer:
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 ________.
Answer:
39) The collectively exhaustive set of events for flipping a coin is ________.
Answer:
40) A ________ organizes numerical data to describe the events of an experiment.
Answer:
41) A Venn diagram depicting two circles that do not overlap or touch in any way represents events that are ________.
Answer:
42) A ________ is the probability of occurence of a single event.
Answer:
43) ________ can enable one to improve marginal probabilities of the occurrence of an event by gathering additional information.
Answer:
44) A succession of events that do not affect each other are ________.
Answer:
45) A ________ probability is the probability that an event will occur given that another event has already occurred.
Answer:
46) In a binomial distribution process, there are ________ possible outcomes.
Answer
47) One of the properties of the ________ distribution is that the probability of success remains constant over time.
Answer:
48) Altered marginal probability of an event based on additional information is a ________ probability.
Answer:
49) The ________ of a random variable is computed by multiplying each possible value of the variable by its probability and summing these products.
Answer:
50) If events A and B are independent, then P(AB) = ________.
Answer:
51) If events A and B are independent, then P(A|B) = ________.
Answer:
52) If two events A and B are not mutually exclusive, then P(A or B) = ________.
Answer:
53) ________ is a measure of dispersion of random variable values about the expected value.
Answer:
54) A continuous random variable can take on a(n) ________ number of values within a given interval.
Answer:
55) The ________ test is a statistical test to see if an observed data fit a particular probability distribution.
Answer:
56) The ________ normal distribution has a mean of 0 and a standard deviation of 1.
Answer:
57) Almost all of the data from a normal distribution fall within ________ standard deviations of the mean.
Answer:
58) The expected value of the standard normal distribution is equal to ________.
Answer:
59) The standard deviation of the standard normal distribution is equal to ________.
Answer:
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?
Answer
61) What is the probability that Jim will not be accepted at either university?
Answer:
62) What is the probability that Jim will be accepted by at least one of the two universities?
Answer:
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
Administrative (AD) 110 10
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?
Answer:
64) If an employee is selected at random, what is the probability that the employee is male and salaried staff?
Answer:
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?
Answer:
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
Answer:
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?
Answer:
68) What is the average number of complaints received per week?
Answer:
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?
Answer:
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?
Answer
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.
Answer:
72) Find the probability that none of the 3 products is successful.
Answer:
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.
Answer:
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.
Answer:
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 ≤ _____)?
Answer:
76) For a standard normal distribution, what is the probability that z is greater than 1.75?
Answer
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?
Answer:
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?
Answer:
79) Which student scored better compared to the rest of their section?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
90) For the normal distribution, the mean plus and minus 1.96 standard deviations will include what percent of the observations?
Answer:
91) What is the area under the normal curve for Z ≥ 1.79?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
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 ________.
Answer:
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.
Answer:
97) What are the differences between deterministic and probabilistic techniques?
Answer:
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?
Answer: 13/20 = 65%
Diff: 1 Page Ref: 508
Section Heading: Fundamentals of Probability
Keywords: cumulative probability distribution
AACSB: Analytic skills
99) What is the cumulative probability for the three shortest commute categories?
Answer
100) What is the average commute time for HOV Lane?
Answer:
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.
Answer:
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?
Answer:
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 ________.
Answer:
104) The probability of winning at least $1000 is ________.
Answer:
105) ________ techniques assume that no uncertainty exists in model parameters.
A) Probability
B) Probabilistic
C) Deterministic
D) Distribution
Answer:
106) ________ probability is an estimate based on personal belief, experience, or knowledge of a situation.
A) Binomial
B) Subjective
C) Marginal
D) Joint
Answer:
Diff: 2 Page Ref: 504
Section Heading: Types of Probability
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.
Answer:
Diff: 2 Page Ref: 503
Section Heading: Types of Probability
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
Answer:
Diff: 1 Page Ref: 505
Section Heading: Fundamentals of Probability
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.
Answer:
Diff: 1 Page Ref: 505
Section Heading: Fundamentals of Probability
Keywords: mutually exclusive events
110) A ________ probability is the probability of a single event occurring.
A) subjective
B) binomial
C) marginal
D) joint
Answer:
Diff: 1 Page Ref: 506
Section Heading: Fundamentals of Probability
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
Answer:
Diff: 1 Page Ref: 505
Section Heading: Fundamentals of Probability
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
Answer:
Diff: 2 Page Ref: 505
Section Heading: Fundamentals of Probability
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
Answer:
Diff: 2 Page Ref: 506
Section Heading: Fundamentals of Probability
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
Administrative (AD) 110 10
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
Answer:
Diff: 2 Page Ref: 508
Section Heading: Fundamentals of Probability
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
Answer:
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
B) adding
C) subtracting
D) dividing
Answer:
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
Answer:
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
Answer:
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
Administrative (AD) 110 10
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
Answer:
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
Answer:
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.
Answer:
Diff: 2 Page Ref: 505
Section Heading: Fundamentals of Probability
Keywords: mutually exclusive events
122) Bayesian analysis involves a(n) ________ probability.
A) a priori
B) posterior
C) joint
D) relative frequency
Answer:
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
Answer:
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.
Answer:
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.
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
Diff: 2 Page Ref: 515
Section Heading: Expected Value
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
Answer:
Diff: 2 Page Ref: 516
Section Heading: Expected Value
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
Answer:
Diff: 1 Page Ref: 519
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 517
Section Heading: The Normal Distribution
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
Answer:
Diff: 1 Page Ref: 511
Section Heading: The Normal Distribution
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%
Answer:
Diff: 3 Page Ref: 520
Section Heading: The Normal Distribution
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%
Answer:
Diff: 1 Page Ref: 520
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 520
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 519
Section Heading: The Normal Distribution
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%
Answer:
Diff: 2 Page Ref: 519
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 520
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 520
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 519
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 519
Section Heading: The Normal Distribution
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
Answer:
Diff: 1 Page Ref: 520
Section Heading: The Normal Distribution
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
Answer:
Diff: 1 Page Ref: 520
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 519
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 520
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 520
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 519
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 516
Section Heading: Expected Value
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
Answer:
Diff: 2 Page Ref: 507-508
Section Heading: Fundamentals of Probability
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
Answer:
Diff: 2 Page Ref: 503
Section Heading: Types of Probability
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.
Answer:
Diff: 1 Page Ref: 506
Section Heading: Fundamentals of Probability
Keywords: mutually exclusive events
Strayer Mat 540 Quiz 1 Solution
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MAT 540 Week 8 Homework Problems – Strayer University New
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MAT 540 Week 8 Chapter 4 Problems
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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.
Program Votes/ Dollar
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
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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
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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.
Answer:
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.
Answer:
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
Answer:
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
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
Diff: 2 Page Ref: 12
Section Heading: Computer Solution
Keywords: spreadsheets
AACSB: Analytic skills
20) Management science techniques focus primarily on observation, model construction, and implementation to find an appropriate solution to a problem.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
30) ________ are known, constant values that are coefficients of variables in equations.
Answer:
31) ________ are pieces of information from the problem environment.
Answer:
32) A ________ is a functional relationship including variables, parameters, and equations.
Answer:
33) Management science techniques include ________ techniques, models that are represented as diagrams, presenting a pictorial representation of the system being analyzed.
Answer:
34) An increase in output typically results in an increase in the ________ cost.
Answer:
35) ________ techniques provide results that contain uncertainty, unlike mathematical programming techniques which are deterministic.
Answer:
36) ________ costs are independent of the volume of goods produced and remain constant.
Answer:
37) The difference between volume multiplied by price and the sum of fixed and variable costs is ________.
Answer:
38) ________ depend on the number of items produced.
Answer:
39) Total revenue minus total cost equals ________.
Answer:
40) The ________ is the volume that equates total revenue with total cost.
Answer:
41) A ________ represents a limitation to achieving maximum profits due to limited resources.
Answer:
42) A ________ programming technique refers to a predetermined set of mathematical steps used to solve a problem.
Answer:
43) One way to test how a management science model reacts to changes in its parameters is to conduct ________ analysis.
Answer:
44) ________ consist of models that are represented as diagrams rather than as strictly mathematical techniques.
Answer:
45) A management science technique that does not assume that all parameters are known with certainty is a(n) ________ technique.
Answer:
46) A ________ is a computer-based system that helps decision-makers address complex problems that involve different parts of an organization and operations.
Answer:
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?
Answer:
48) Researchers at John H. Stroger, Jr. Hospital of Cook County used ________ to address the problem of healthcare-associated infections in hospitals.
Answer
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
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?
Answer
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.
Answer:
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.
Answer: R(x) = 165x
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?
Answer:
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.
Answer:
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?
Answer:
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.
Answer:
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?
Answer:
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?
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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?
Answer:
69) What are some different types of decision support systems?
Answer:
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?
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
74) A model is a functional relationship that includes:
- A) variables.
- B) parameters.
- C) equations.
- D) all of the above
Answer:
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
Answer:
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
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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
Answer:
81) ________ involves determining the functional relationship between variables, parameters, and equations.
- A) Problem observation
- B) Problem definition
- C) Model construction
- D) Model solution
Answer:
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
Answer:
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.
- D) access to a computer.
Answer:
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.
- B) railroads.
- C) politics.
- D) manufacturing.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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
Answer:
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.
Answer:
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.
Answer:
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
Answer:
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.
Answer:
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.
Answer:
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
Answer:
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
Answer:
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.
Answer:
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.
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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.
Answer:
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?
Answer:
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.
Answer:
Diff: 2 Page Ref: 12
Section Heading: Computer Solution
Keywords: computer solution, spreadsheets
AACSB: Analytic skills
109) A technique that assumes certainty in its solution is referred to as
- A) stochastic.
- B) probabilistic.
- C) deterministic.
- D) parametric.
Answer:
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.
Answer:
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.
Answer:
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
Answer:
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
Answer:
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
Answer:
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) 4x1 + 3x2 + 2x3 ≤ 24
Answer:
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.
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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?
- A) an Excel spreadsheet
- B) an ERP
- C) QM for Windows
- D) OLAP
Answer:
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.
Answer:
Diff: 1 Page Ref: 503
Section Heading: Types of Probability
Keywords: deterministic techniques
2) Probabilistic techniques assume that no uncertainty exists in model parameters.
Answer:
Diff: 1 Page Ref: 503
Section Heading: Types of Probability
Keywords: probabilistic techniques
3) Objective probabilities that can be stated prior to the occurrence of an event are classical or a priori.
Answer:
Diff: 2 Page Ref: 503
Section Heading: Types of Probability
Keywords: objective probabilities, classical probabilities
4) Objective probabilities that are stated after the outcomes of an event have been observed are relative frequencies.
Answer:
Diff: 2 Page Ref: 503
Section Heading: Types of Probability
Keywords: relative frequencies
5) Relative frequency is the more widely used definition of objective probability.
Answer:
Diff: 1 Page Ref: 504
Section Heading: Types of Probability
Keywords: relative frequencies
6) Subjective probability is an estimate based on personal belief, experience, or knowledge of a situation.
Answer:
Diff: 2 Page Ref: 504
Section Heading: Types of Probability
Keywords: subjective probability
7) An experiment is an activity that results in one of several possible outcomes.
Answer:
Diff: 1 Page Ref: 505
Section Heading: Fundamentals of Probability
Keywords: experiment
8) The events in an experiment are mutually exclusive if only one can occur at a time.
Answer:
Diff: 1 Page Ref: 505
Section Heading: Fundamentals of Probability
Keywords: mutually exclusive events
9) In a given experiment, the probabilities of all mutually exclusive events sum to one.
Answer:
Diff: 1 Page Ref: 505
Section Heading: Fundamentals of Probability
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.
Answer:
Diff: 2 Page Ref: 506
Section Heading: Fundamentals of Probability
Keywords: collectively exhaustive events
11) A marginal probability is the probability of a single event occurring.
Answer:
Diff: 1 Page Ref: 506
Section Heading: Fundamentals of Probability
Keywords: marginal probability
12) A Venn diagram visually displays mutually exclusive and non-mutually exclusive events.
Answer:
Diff: 2 Page Ref: 506
Section Heading: Fundamentals of Probability
Keywords: Venn diagram
13) A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously.
Answer:
Diff: 2 Page Ref: 506
Section Heading: Fundamentals of Probability
Keywords: joint probability
14) A conditional probability is the probability that an event occurs given that another event has already occurred.
Answer:
Diff: 1 Page Ref: 508
Section Heading: Statistical Independence and Dependence
Keywords: conditional probability
15) Conditional probabilities are shown in Venn diagrams.
Answer:
Diff: 1 Page Ref: 506
Section Heading: Fundamentals of Probability
Keywords: conditional probability
16) Probability trees are used only to compute conditional probabilities.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
Diff: 1 Page Ref: 517
Section Heading: The Normal Distribution
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.
Answer:
Diff: 1 Page Ref: 519
Section Heading: The Normal Distribution
Keywords: normal distribution
AACSB: Analytic skills
21) Another name for the mean of a probability distribution is its expected value.
Answer:
Diff: 1 Page Ref: 516
Section Heading: Expected Value
Keywords: expected value
AACSB: Analytic skills
22) The expected value of a discrete random variable is greater than or equal to zero.
Answer:
Diff: 1 Page Ref: 516
Section Heading: Expected Value
Keywords: expected value
23) The variance of a discrete random variable is always greater than or equal to zero.
Answer:
Diff: 1 Page Ref: 516
Section Heading: Expected Value
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.
Answer:
Diff: 1 Page Ref: 516
Section Heading: Expected Value
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.
Answer:
Diff: 1 Page Ref: 516
Section Heading: Expected Value
Keywords: variance
AACSB: Analytic skills
26) For a typical normally distributed random variable, the standard deviation is equal to the variance.
Answer:
Diff: 1 Page Ref: 518
Section Heading: The Normal Distribution
Keywords: normal distribution
27) A normally distributed random variable has a mean of zero and a standard deviation of one.
Answer:
Diff: 1 Page Ref: 517-518
Section Heading: The Normal Distribution
Keywords: normal distribution
28) The standard normal distribution has a mean of one and a standard deviation of zero.
Answer:
Diff: 1 Page Ref: 519
Section Heading: The Normal Distribution
Keywords: standard normal distribution
29) The area under the normal curve represents probability.
Answer:
Diff: 1 Page Ref: 518
Section Heading: The Normal Distribution
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.
Answer:
Diff: 1 Page Ref: 518
Section Heading: The Normal Distribution
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.
Answer:
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.
Answer:
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 ________.
Answer: lassical or a priori
Diff: 1 Page Ref: 503
Section Heading: Types of Probability
Keywords: probabilistic techniques, objective/classical probabilities
34) ________ probability is an estimate based on a personal belief, experience, and knowledge of a situation.
Answer:
35) The events in an experiment are ________ if only one can occur at a time.
Answer:
36) The term for including all possible events that can occur in an experiment is ________.
Answer:
37) The cumulative probability for all six outcomes of tossing a fair die should end with the value ________.
Answer:
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 ________.
Answer:
39) The collectively exhaustive set of events for flipping a coin is ________.
Answer:
40) A ________ organizes numerical data to describe the events of an experiment.
Answer:
41) A Venn diagram depicting two circles that do not overlap or touch in any way represents events that are ________.
Answer:
42) A ________ is the probability of occurence of a single event.
Answer:
43) ________ can enable one to improve marginal probabilities of the occurrence of an event by gathering additional information.
Answer:
44) A succession of events that do not affect each other are ________.
Answer:
45) A ________ probability is the probability that an event will occur given that another event has already occurred.
Answer:
46) In a binomial distribution process, there are ________ possible outcomes.
Answer
47) One of the properties of the ________ distribution is that the probability of success remains constant over time.
Answer:
48) Altered marginal probability of an event based on additional information is a ________ probability.
Answer:
49) The ________ of a random variable is computed by multiplying each possible value of the variable by its probability and summing these products.
Answer:
50) If events A and B are independent, then P(AB) = ________.
Answer:
51) If events A and B are independent, then P(A|B) = ________.
Answer:
52) If two events A and B are not mutually exclusive, then P(A or B) = ________.
Answer:
53) ________ is a measure of dispersion of random variable values about the expected value.
Answer:
54) A continuous random variable can take on a(n) ________ number of values within a given interval.
Answer:
55) The ________ test is a statistical test to see if an observed data fit a particular probability distribution.
Answer:
56) The ________ normal distribution has a mean of 0 and a standard deviation of 1.
Answer:
57) Almost all of the data from a normal distribution fall within ________ standard deviations of the mean.
Answer:
58) The expected value of the standard normal distribution is equal to ________.
Answer:
59) The standard deviation of the standard normal distribution is equal to ________.
Answer:
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?
Answer
61) What is the probability that Jim will not be accepted at either university?
Answer:
62) What is the probability that Jim will be accepted by at least one of the two universities?
Answer:
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
Administrative (AD) 110 10
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?
Answer:
64) If an employee is selected at random, what is the probability that the employee is male and salaried staff?
Answer:
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?
Answer:
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
Answer:
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?
Answer:
68) What is the average number of complaints received per week?
Answer:
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?
Answer:
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?
Answer
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.
Answer:
72) Find the probability that none of the 3 products is successful.
Answer:
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.
Answer:
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.
Answer:
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 ≤ _____)?
Answer:
76) For a standard normal distribution, what is the probability that z is greater than 1.75?
Answer
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?
Answer:
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?
Answer:
79) Which student scored better compared to the rest of their section?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
90) For the normal distribution, the mean plus and minus 1.96 standard deviations will include what percent of the observations?
Answer:
91) What is the area under the normal curve for Z ≥ 1.79?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
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 ________.
Answer:
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.
Answer:
97) What are the differences between deterministic and probabilistic techniques?
Answer:
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?
Answer: 13/20 = 65%
Diff: 1 Page Ref: 508
Section Heading: Fundamentals of Probability
Keywords: cumulative probability distribution
AACSB: Analytic skills
99) What is the cumulative probability for the three shortest commute categories?
Answer
100) What is the average commute time for HOV Lane?
Answer:
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.
Answer:
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?
Answer:
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 ________.
Answer:
104) The probability of winning at least $1000 is ________.
Answer:
105) ________ techniques assume that no uncertainty exists in model parameters.
- A) Probability
- B) Probabilistic
- C) Deterministic
- D) Distribution
Answer:
106) ________ probability is an estimate based on personal belief, experience, or knowledge of a situation.
- A) Binomial
- B) Subjective
- C) Marginal
- D) Joint
Answer:
Diff: 2 Page Ref: 504
Section Heading: Types of Probability
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.
Answer:
Diff: 2 Page Ref: 503
Section Heading: Types of Probability
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
Answer:
Diff: 1 Page Ref: 505
Section Heading: Fundamentals of Probability
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.
Answer:
Diff: 1 Page Ref: 505
Section Heading: Fundamentals of Probability
Keywords: mutually exclusive events
110) A ________ probability is the probability of a single event occurring.
- A) subjective
- B) binomial
- C) marginal
- D) joint
Answer:
Diff: 1 Page Ref: 506
Section Heading: Fundamentals of Probability
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
Answer:
Diff: 1 Page Ref: 505
Section Heading: Fundamentals of Probability
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
Answer:
Diff: 2 Page Ref: 505
Section Heading: Fundamentals of Probability
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
Answer:
Diff: 2 Page Ref: 506
Section Heading: Fundamentals of Probability
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
Administrative (AD) 110 10
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
Answer:
Diff: 2 Page Ref: 508
Section Heading: Fundamentals of Probability
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
Answer:
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
- B) adding
- C) subtracting
- D) dividing
Answer:
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
Answer:
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
Answer:
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
Administrative (AD) 110 10
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
Answer:
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
Answer:
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.
Answer:
Diff: 2 Page Ref: 505
Section Heading: Fundamentals of Probability
Keywords: mutually exclusive events
122) Bayesian analysis involves a(n) ________ probability.
- A) a priori
- B) posterior
- C) joint
- D) relative frequency
Answer:
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
Answer:
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.
Answer:
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.
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
Diff: 2 Page Ref: 515
Section Heading: Expected Value
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
Answer:
Diff: 2 Page Ref: 516
Section Heading: Expected Value
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
Answer:
Diff: 1 Page Ref: 519
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 517
Section Heading: The Normal Distribution
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
Answer:
Diff: 1 Page Ref: 511
Section Heading: The Normal Distribution
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%
Answer:
Diff: 3 Page Ref: 520
Section Heading: The Normal Distribution
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%
Answer:
Diff: 1 Page Ref: 520
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 520
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 519
Section Heading: The Normal Distribution
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%
Answer:
Diff: 2 Page Ref: 519
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 520
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 520
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 519
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 519
Section Heading: The Normal Distribution
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
Answer:
Diff: 1 Page Ref: 520
Section Heading: The Normal Distribution
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
Answer:
Diff: 1 Page Ref: 520
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 519
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 520
Section Heading: The Normal Distribution
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
Answer:
Diff: 2 Page Ref: 520
Section Heading: The Normal Distribution
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
Answer:
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
Answer:
150) What is the probability that Mr. Lane makes it home in under thirty minutes?
- A) .15
- B) .35
- C) .20
- D) .55
Answer:
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?
- A) subjective probability
- B) conjecture probability
- C) objective probability
- D) reflexive probability
Answer:
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.
Answer:
Introduction to Management Science, (Taylor)
Chapter 12 Decision Analysis
1) A state of nature is an actual event that may occur in the future.
Answer:
2) A payoff table is a means of organizing a decision situation, including the payoffs from different decisions given the various states of nature.
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3) The maximax criterion results in the maximum of the maximum payoffs.
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4) The maximin approach involves choosing the alternative with the highest payoff.
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5) Regret is the difference between the payoff from the best decision and all other decision payoffs.
Answer:
6) The minimax regret criterion minimizes the maximum regret.
Answer:
7) The minimax regret criterion maximizes the minimum regret.
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8) The Hurwicz criterion is a compromise between the maximax and maximin criteria.
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9) The Hurwicz criterion is a compromise between the minimax and minimin criteria.
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10) The coefficient of optimism is a measure of the decision maker’s optimism.
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11) The Hurwicz criterion multiplies the best payoff by the coefficient of optimism.
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12) The Hurwicz criterion multiplies the worst payoff by the coefficient of optimism.
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13) A dominant decision is one that has a better payoff than another decision under each state of nature.
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14) The appropriate criterion is dependent on the risk personality and philosophy of the decision maker.
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15) The maximax criterion is optimistic.
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16) The maximin criterion maximizes the minimum regret.
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17) The minimax criterion minimizes the maximum payoff.
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18) Regret and opportunity loss mean the same thing.
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19) The equal likelihood criterion assigns a probability of 0.5 to each state of nature.
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20) Expected opportunity loss is the expected value of the regret for each decision.
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21) When using decision trees, branches with the greatest expected value are selected.
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22) A decision tree is a diagram consisting of circular decision nodes, square probability nodes, and branches.
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23) Additional information is used to alter the marginal probability of occurrence of an event in Bayesian analysis.
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24) A conditional probability is the probability that two events will occur simultaneously.
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25) A posterior probability is the likelihood that an event has occurred after the decision maker has reached a decision.
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26) Events are mutually exclusive if one, and only one, can occur at a time.
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27) The expected value of perfect information divided by the expected value of sample information is the efficiency of perfect information.
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28) When the ________ criterion is used, the maximum of the maximum payoffs is selected.
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29) When the ________ criterion is used, the maximum of the minimum payoffs is selected
Answer:
30) ________ is the difference between the payoff from the best decision and all other decision payoffs.
Answer:
31) The ________ is a compromise between the maximax and the maximin criterion.
Answer:
32) The ________ is a measure of the decision makers optimism.
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33) A(n) ________ decision is one that has a better payoff than another decision under each state of nature.
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34) A ________ structures decisions with a series of nodes.
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35) The ________ of sample information is the ratio of the expected value of sample information to the expected value of perfect information.
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36) When the ________ criterion is used, the decision maker selects the decision alternative that minimizes the maximum regret.
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37) A ________ decision tree illustrates a situation requiring a series of decisions.
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38) ________ is a measure of personal satisfaciton derived from money.
Answer:
39) People who forgo a high expected value to avoid a disaster with a low probability are ________.
Answer:
40) The efficiency of sample information is the ratio of the expected value of sample information to ________.
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41) The difference in the expected value with additional information and without additional information is ________.
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42) The efficiency of sample information multiplied by the expected value of perfect information is ________.
Answer:
43) If only one of three events can occur at any given time, the events are ________.
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44) If the decision maker receives additional information such that the marginal probabilities of certain events should be modified, these revised probabilites are called ________.
Answer:
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?
Answer:
46) If the group is conservative, what decision will they make?
Answer:
47) If the group chooses to minimize their maximum regret, what activity will they choose?
Answer:
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?
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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?
Answer:
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?
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51) What decision would be made under maximin?
Answer:
52) What decision would be made under minimax regret?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
56) If the manager uses minimax regret as the decision criterion, which of the alternatives would she choose?
Answer:
57) Use the expected value criterion to select the best alternative. Assume that the probability of S2 is equal to 0.4.
Answer
58) Compute the expected value of perfect information assuming that the probability of S2
is equal to 0.4.
Answer:
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?
Answer:
60) If he uses the minimax regret criterion, how many new workers will he hire?
Answer: 2
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?
Answer:
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?
Answer:
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.
Answer:
64) Draw a decision tree and determine the payoff for each decision and event node. Which alternative should the manufacturer choose?
Answer:
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.
Answer:
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?
Answer:
67) What action would you choose according to maximin criterion?
Answer:
68) Construct the regret table.
Answer:
69) What action would you choose according to minimax regret criterion?
Answer:
70) What action would you choose according to expected value criterion?
Answer:
71) What is the maximum amount that you would be willing to pay for perfect information?
Answer:
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.
Answer:
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?
Answer:
74) Pedro is extremely pessimistic. Which decision making criterion would he naturally select and what conclusion would he recommend to Napoleon? Why?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
78) Consider the following decision tree.
What is the expected value at node 4?
Answer: $600
79) Consider the following decision tree.
What is the value associated with node 3?
Answer:
80) Consider the following decision tree.
Which decision, A or B, is best? What is the expected value of this decision?
Answer:
81) 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.
Answer:
82) 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.
Answer:
83) 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
Answer:
84) The ________ minimizes the maximum regret.
- A) maximax regret criterion
- B) minimax regret criterion
- C) minimin regret criterion
- D) maximin regret criterion
Answer:
85) The minimax regret criterion
- A) maximizes the minimum regret.
- B) minimizes the minimum regret.
- C) minimizes the maximum regret.
- D) maximizes the maximum regret.
Answer:
86) 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.
Answer:
87) 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.
Answer:
88) The term opportunity loss is most closely related to
- A) maximin regret.
- B) maximax regret.
- C) minimax regret.
- D) minimin regret.
Answer:
89) The Hurwicz criterion is a compromise
- A) between the maximin and minimax criteria.
- B) between the minimax and maximax criteria.
- C) between the maximax and maximin criteria.
- D) none of the above
Answer:
90) 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
Answer:
91) The basic decision environment categories are
- A) certainty.
- B) risk.
- C) uncertainty.
- D) all of the above
Answer:
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?
- A) maximax
- B) maximin
- C) minimax regret
- D) equally likely
Answer:
93) Under which decision making criterion is Texas Tech University the optimal decision?
- A) maximax
- B) maximin
- C) minimax regret
- D) equally likely
Answer:
94) Under which criterion is Seattle University the optimal decision?
- A) maximax
- B) maximin
- C) minimax regret
- D) equally likely
Answer:
95) Under which criterion is Northeastern State University the optimal decision?
- A) maximax
- B) maximin
- C) minimax regret
- D) equally likely
Answer:
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?
- A) Vanderbilt University
- B) Texas Tech University
- C) Seattle University
- D) Northeastern State University
Answer:
97) The basic decision environment categories are
- A) certainty and risk.
- B) risk and uncertainty.
- C) certainty and uncertainty.
- D) certainty, uncertainty and risk.
Answer:
98) The Hurwicz criterion
- A) multiplies the worst payoff by one minus the coefficient of optimism.
- B) multiplies the best payoff by one minus the coefficient of optimism.
- C) is a compromise between the minimax and maximin criteria.
- D) all of the above
Answer:
99) The appropriate criterion is dependent on
- A) the risk personality of the decision maker
- B) the number of nodes in the decision tree.
- C) the magnitude of the payoffs.
- D) none of the above
Answer:
100) The ________ is a measure of the decision maker’s optimism.
- A) equal likelihood criterion
- B) dominant decision
- C) coefficient of optimism
- D) opportunity loss
Answer:
101) 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
Answer:
102) A ________ is one that has a 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
Answer:
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
- A) Buy.
- B) Rent.
- C) Lease.
- D) Brisk.
Answer:
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
- A) Buy.
- B) Rent.
- C) Lease.
- D) Brisk.
Answer:
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
- A) Buy.
- B) Rent.
- C) Lease.
- D) Brisk.
Answer:
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:
- A) 12
- B) 55
- C) 57
- D) 69
Answer:
107) 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
Answer:
108) 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
Answer:
109) 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.
Answer:
110) 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) bid price
Answer:
111) A decision tree is a diagram consisting of
- A) branch angles that vary as likelihoods increase.
- B) triangle probability nodes.
- C) branches representing decision alternatives.
- D) perfect information.
Answer:
112) 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) decision making under certainty
Answer:
113) A ________ probability is the probability that an event will occur given that another event has already occurred.
- A) posterior
- B) conditional
- C) marginal
- D) low
Answer:
114) 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
Answer:
115) 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.
Answer:
116) The expected value of sample information
- A) is never more than EVPI.
- B) can be greater or less than EVPI.
- C) can be positive or negative.
- D) is equivalent to the EVPI.
Answer:
117) 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.
Answer:
118) 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.
Answer:
119) Utiles are units of ________ measures of utility.
- A) quantitative
- B) objective
- C) subjective
- D) qualitative
Answer:
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?
- A) 0.8
- B) 0.5
- C) 0.4
- D) 0.2
Answer:
121) 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
Answer:
122) How many units of Product A can they expect to sell?
- A) 20,000
- B) 17,000
- C) 16,000
- D) 15,000
Answer:
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.
Answer:
2) Monte Carlo is a technique for selecting numbers randomly from a probability distribution.
Answer:
3) The Monte Carlo process is analogous to gambling devices.
Answer:
4) In the Monte Carlo process, values for a random variable are generated by sampling from a probability distribution.
Answer:
5) A long period of real time can be represented by a short period of simulated time.
Answer:
6) Random numbers are equally likely to occur.
Answer:
7) Simulation results will always equal analytical results if 30 trials of the simulation have been conducted.
Answer:
8) It’s often difficult to validate that the results of a simulation truly replicate reality.
Answer:
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.
Answer:
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.
Answer:
12) Random numbers are typically generated on the computer using a numerical technique.
Answer:
13) A table of random numbers must be normally distributed and efficiently generated.
Answer:
14) When using Excel to simulate a system, it is necessary to compute only the probability (relative frequency) distribution.
Answer:
15) Excel can only be used to simulate systems that can be represented by continuous random variables.
Answer:
16) In Excel the VLOOKUP function is used to determine values for continuous random variables.
Answer:
17) Developing the cumulative probability distribution helps to determine random number ranges.
Answer:
18) Starting conditions have no impact on the validity of a simulation model.
Answer:
19) Simulations should always be started with an empty system.
Answer:
20) Manual simulation is limited because of the amount of real time required to simulate even one trial.
Answer:
21) Applications of simulation models reflecting continuous distributions are more common than those of models employing discrete distributions.
Answer:
22) In a continuous probability function, the area under the curve represents the probability of occurrence of the random variable.
Answer:
23) Cumulative probabilities are analogous to the discrete ranges of random numbers used in the Monte Carlo process.
Answer:
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.
Answer:
25) ________ is a technique for selecting numbers randomly from a probability distribution.
Answer:
26) Developing the ________ probability distribution helps to determine random number ranges.
Answer:
27) Random numbers of a mathematical process instead of a physical process are ________ numbers.
Answer:
28) Simulation models must be ________ to make sure they are accurately replicating the system being simulated.
Answer:
29) A table of random numbers must be ________ distributed, efficiently generated, and absent of patterns.
Answer:
30) The ________ command is used in generating the random numbers with Excel.
Answer:
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.
Answer:
32) ________ is a risk analysis and forecasting program that uses Monte Carlo simulation.
Answer:rystal
33) ________, ________, and ________ are common applications of simulation.
Answer:
34) In the Monte Carlo process, values for a random variable are generated by sampling from a(n) ________.
Answer:
35) A long period of real time is represented by a short period of ________.
Answer:
36) The Monte Carlo process is analogous to and derives its name from ________.
Answer:
37) ________ are numbers equally likely to be chosen from a large population of numbers.
Answer:
38) A random number table features numbers that are derived from a(n) ________ process.
Answer:
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 ________.
Answer:
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.
Answer:
41) Determine the drying time for these 5 random numbers: 0.53, 0.95, 0.97, 0.96, and 0.07.
Answer:
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.
Answer:
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
Answer:
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 |
Answer:
45) If f(x) = 2x, what is the equation for generating x, given the random number r?
Answer:
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.
Answer:
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?
Answer:
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.
Answer:
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.
Answer:
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?
Answer:
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.
Answer:
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.
Answer:
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 |
Answer:
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.
Answer:
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?
Answer:
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?
Answer:
57) If the first four random numbers are 17, 33, 64, and 8, what is the average number of weeks?
Answer:
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?
Answer:
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?
Answer:
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?
Answer:
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 |
Answer:
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.
Answer:
63) Analogue simulation replaces a physical system with an analogous physical system that is ________ to manipulate.
- A) harder
- B) easier
- C) equally difficult
- D) more expensive
Answer:
64) ________ is a technique for selecting numbers randomly from a probability distribution.
- A) Marseille
- B) Monaco
- C) Monte Carlo
- D) Analogue simulation
Answer:
65) 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
Answer:
66) The ________ process is analogous to gambling devices.
- A) Simulation
- B) Monte Carlo
- C) Monaco
- D) none of the above
Answer:
67) ________ numbers are numbers derived from a mathematical process that appear to be random.
- A) Random
- B) Pseudorandom
- C) Randomized
- D) Semi-random
Answer:
68) Pseudorandom numbers exhibit a ________ in order to be considered truly random.
- A) limited number of possible outcomes
- B) uniform distribution
- C) detectable pattern
- D) detectable run of certain numbers
Answer:
69) ________ 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
Answer:
70) 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.
Answer:
71) 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) the events dictate the seed number of the random number stream.
Answer:
72) ________ 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
Answer:
73) Simulation does not usually provide recommended decisions. Instead it provides
- A) operating characteristics.
- B) optimal solutions.
- C) realistic results.
- D) system parameters.
Answer:
74) 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
Answer:
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:
- A) 0
- B) 1
- C) 2
- D) 3
Answer:
76) If the simulation begins with the second random number, the simulated value for demand would be:
- A) 1
- B) 2
- C) 3
- D) 4
Answer:
77) 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
Answer:
78) 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.
Answer:
79) Simulations are normally done
- A) manually.
- B) in a casino.
- C) by a spreadsheet.
- D) on the computer.
Answer:
80) 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
Answer:
81) A table of random numbers must be
- A) in descending order.
- B) efficiently generated.
- C) normally distributed.
- D) in ascending order.
Answer:
82) Developing the cumulative probability distribution helps to determine
- A) simulation numbers.
- B) data sets.
- C) random number ranges.
- 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:
- A) 1 minute
- B) 2 minutes
- C) 2.5 minutes
- D) 3 minutes
Answer:
84) Average utilization is:
- A) 67%
- B) 72.5%
- C) 83.4%
- D) 95%
Answer:
85) ________ 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
Answer:
86) 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
Answer:
87) Sometimes manual simulation of several trials is ________ way to validate a simulation.
- A) a good
- B) a bad
- C) no
- D) the only
Answer:
88) Unlike optimization models, simulation provides
- A) recommendations.
- B) operating characteristics.
- C) suggestions.
- D) solutions .
Answer:
89) A limitation of simulation is that
- A) models are typically well-structured and must be developed for problems that are also well-structured.
- B) it is usually possible to realistically validate simulation results.
- C) model building is costly and time-consuming.
- D) it is more difficult to manipulate the elements of a computer simulation than the actual system.
Answer:
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?
- A) 425
- B) 442
- C) 440
- D) 475
Answer:
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?
- A) 425
- B) 442
- C) 440
- D) 475
Answer:
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?
- A) 22
- B) 23
- C) 24
- D) 25
Answer:
93) 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
Answer:
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:
- A) 6
- B) 7
- C) 8
- D) 9
Answer:
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?
- A) .25
- B) .35
- C) .36
- D) .71
Answer:
96) What is the probability that there are more than 3 breakdowns?
- A) .07
- B) .10
- C) .22
- D) .25
Answer:
97) 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
Answer:
98) A 95% confidence interval is (54.5, 57.5) based on a sample size of 25. What is the sample standard deviation?
- A) 3.826
- B) 19.132
- C) 8.973
- D) 11.646
Answer:
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?
- A) (44.13, 55.87)
- B) (46.83, 53.17)
- C) (40.67, 59.32)
- D) (48.22, 51.78)
Answer:
100) 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) project management.
Answer:
101) 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) operations management.
Answer:
Introduction to Management Science, (Taylor)
Chapter 15 Forecasting
1) A trend is a gradual, long-term, up-or-down movement of demand.
Answer:
Diff: 1 Page Ref: 690
Section Heading: Forecasting Components
Keywords: trend, forecasting components
2) A seasonal pattern is an up-and-down repetitive movement within a trend occurring periodically.
Answer:
Diff: 1 Page Ref: 690
Section Heading: Forecasting Components
Keywords: seasonal pattern, forecasting components
3) Random variations are movements that are not predictable and follow no pattern.
Answer:
Diff: 2 Page Ref: 690
Section Heading: Forecasting Components
Keywords: random variations, forecasting components
4) The basic types of forecasting methods include time series, regression, and qualitative methods.
Answer:
Diff: 2 Page Ref: 691
Section Heading: Forecasting Components
Keywords: types of forecasting methods
5) Time series is a category of statistical techniques that uses historical data to predict future behavior.
Answer:
Diff: 1 Page Ref: 691
Section Heading: Forecasting Components
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.
Answer:
Diff: 2 Page Ref: 691
Section Heading: Forecasting Components
Keywords: regression methods
7) Qualitative methods use management judgment, expertise, and opinion to make forecasts.
Answer:
Diff: 2 Page Ref: 691
Section Heading: Forecasting Components
Keywords: qualitative methods
8) Qualitative methods are the least common type of forecasting method for the long-term strategic planning process.
Answer:
Diff: 1 Page Ref: 691
Section Heading: Forecasting Components
Keywords: qualitative methods
9) A cycle is an up-or-down movement in demand that repeats itself in less than 1 year.
Answer:
Diff: 1 Page Ref: 690
Section Heading: Forecasting Components
Keywords: regression methods
10) Seasonal patterns are observed only during the four seasons – winter, spring, summer, and fall.
Answer:
Diff: 1 Page Ref: 690
Section Heading: Forecasting Components
Keywords: time series methods
11) The Delphi method develops a consensus forecast about what will occur in the future.
Answer:
Diff: 2 Page Ref: 693
Section Heading: Forecasting Components
Keywords: Delphi method, qualitative methods
12) Technological forecasting helps determine the technological feasibility of new products by surveying large numbers of consumers.
Answer:
Diff: 1 Page Ref: 693
Section Heading: Forecasting Components
Keywords: technological forecasting
13) Irregular variations exhibit no pattern.
Answer:
Diff: 1 Page Ref: 690
Section Heading: Forecasting Components
Keywords: forecasting components, irregular variation
14) Data cannot exhibit both trend and cyclical patterns.
Answer:
Diff: 1 Page Ref: 690
Section Heading: Forecasting Components
Keywords: forecasting components, trend, cyclical
15) Time series methods assume that what has occurred in the past will continue to occur in the future.
Answer:
Diff: 1 Page Ref: 693
Section Heading: Time Series Methods
Keywords: time series methods
16) Moving averages are good for stable demand with no pronounced behavioral patterns.
Answer:
Diff: 2 Page Ref: 693
Section Heading: Time Series Methods
Keywords: moving averages
17) Longer-period moving averages react more slowly to recent demand changes than do shorter-period moving averages.
Answer:
Diff: 2 Page Ref: 695
Section Heading: Time Series Methods
Keywords: moving averages
AACSB: Analytic skills
18) Shorter-period moving averages react more slowly to recent demand changes than do longer-period moving averages.
Answer:
Diff: 2 Page Ref: 695
Section Heading: Time Series Methods
Keywords: moving averages
AACSB: Analytic skills
19) In a weighted moving average, weights must sum to 1.
Answer:
Diff: 1 Page Ref: 696
Section Heading: Time Series Methods
Keywords: moving averages, weighted moving average, time series methods
20) Adjusted exponential smoothing is an exponential smoothing forecast adjusted for seasonality.
Answer:
Diff: 1 Page Ref: 700
Section Heading: Time Series Methods
Keywords: adjusted exponential smoothing
21) If average forecast error is positive, it indicates that the forecast is biased high.
Answer:
Diff: 2 Page Ref: 708
Section Heading: Forecast Accuracy
Keywords: forecast error
AACSB: Analytic skills
22) Regression is used to relate one variable to one or more variables.
Answer:
Diff: 1 Page Ref: 713
Section Heading: Regression Methods
Keywords: regression methods, linear regression
23) The dependent variable in linear regression is usually designated as the x variable.
Answer:
Diff: 2 Page Ref: 713
Section Heading: Regression Methods
Keywords: regression methods, linear regression
24) In the regression equation y=a+bx, the slope of the equation is x.
Answer:
Diff: 2 Page Ref: 713
Section Heading: Regression Methods
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.
Answer:
Diff: 2 Page Ref: 715
Section Heading: Regression Methods
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.
Answer:
Diff: 2 Page Ref: 713
Section Heading: Regression Methods
Keywords: regression methods, linear regression
27) ________ is a gradual, long-term, upward or downward movement of demand.
Answer: Trend
Diff: 2 Page Ref: 690
Section Heading: Forecasting Components
Keywords: trend
28) A(n) ________ forecast typically encompass a period longer than one year.
Answer: long-range
Diff: 2 Page Ref: 690
Section Heading: Forecasting Components
Keywords: long range forecasts
29) Daily operations are assisted by ________-range forecasting
Answer: short
Diff: 1 Page Ref: 690
Section Heading: Forecasting Components
Keywords: short range forecasts
30) Unpredictable movements in demand that follow no pattern are ________.
Answer: random variations
Diff: 1 Page Ref: 690
Section Heading: Forecasting Components
Keywords: forecasting components, irregular variation
31) The major types of forecasting methods are ________, ________, and ________.
Answer: time series, regression, qualitative
Diff: 1 Page Ref: 691
Section Heading: Forecasting Components
Keywords: forecasting methods
32) Knowledgeable individuals bring their opinions to bear in ________, a qualitative method of forecasting.
Answer: the Delphi method
Diff: 1 Page Ref: 693
Section Heading: Forecasting Components
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) ________.
Answer:ycle
Diff: 1 Page Ref: 690
Section Heading: Forecasting Components
Keywords: forecasting components, trend, cyclical
34) ________ error is the sum of the forecast errors.
Answer:umulative
Diff: 2 Page Ref: 708
Section Heading: Forecast Accuracy
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.
Answer: short-range
Diff: 2 Page Ref: 690
Section Heading: Forecasting Components
Keywords: short range forecasts
36) A(n) ________ is an up-and-down repetitive movement within a trend occurring periodically.
Answer: seasonal pattern
Diff: 2 Page Ref: 690
Section Heading: Forecasting Components
Keywords: seasonal pattern, forecasting components
37) ________ relates demand to two or more independent variables.
Answer: Multiple regression
Diff: 2 Page Ref: 719
Section Heading: Regression Methods
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.
Answer: multicollinearity
Diff: 2 Page Ref: 722
Section Heading: Regression Methods
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, ________.
Answer: increases
Diff: 2 Page Ref: 698
Section Heading: Time Series
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.
Answer: greater
Diff: 2 Page Ref: 698
Section Heading: Time Series
Keywords: simple exponential smoothing
AACSB: Analytic skills
41) ________ measures the strength of the relationship between two variables.
Answer:orrelation
Diff: 2 Page Ref: 716
Section Heading: Regression Methods
Keywords: correlation, regression methods, linear regression model
42) The ________ is the percentage of variation in the dependent variable that results from the independent variable.
Answer:oefficient of determination
Diff: 2 Page Ref: 716
Section Heading: Regression Methods
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.
Answer: slowly
Diff: 2 Page Ref: 694
Section Heading: Time Series
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.
Answer: Random variations
Diff: 2 Page Ref: 690
Section Heading: Time Series
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.
Answer: MAD or mean absolute deviation
Diff: 1 Page Ref: 706
Section Heading: Forecast Accuracy
Keywords: forecast error, MAD
46) The ________ is the average of the sum of the squared errors.
Answer: MSE or mean squared error
Diff: 1 Page Ref: 708
Section Heading: Forecast Accuracy
Keywords: forecast error, MSE
47) MAPD measures ________.
Answer: the absolute error as a percentage of the actual (demand) data
Diff: 2 Page Ref: 707
Section Heading: Forecast Accuracy
Keywords: forecast error, MAPD
48) ________ is a type of exponential smoothing that can also include trend.
Answer:djusted exponential smoothing
Diff: 1 Page Ref: 700
Section Heading: Time Series
Keywords: adjusted exponential smoothing
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.
Answer: 211.67
Diff: 2 Page Ref: 694
Section Heading: Time Series
Keywords: moving averages, time series methods
AACSB: Analytic skills
50) Compute a 3-period moving average for period 6.
Answer: 246.67
Diff: 2 Page Ref: 694
Section Heading: Time Series
Keywords: moving averages, time series methods
AACSB: Analytic skills
51) Compute a 3-period moving average for period 7.
Answer: 283.33
Diff: 2 Page Ref: 694
Section Heading: Time Series
Keywords: moving averages, time series methods
AACSB: Analytic skills
52) Compute a 5-period moving average for period 6.
Answer: 237
Diff: 3 Page Ref: 694
Section Heading: Time Series
Keywords: moving averages, time series methods
AACSB: Analytic skills
53) Compute a 5-period moving average for period 7.
Answer: 257
Diff: 3 Page Ref: 694
Section Heading: Time Series
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.
Answer: 91
Diff: 1 Page Ref: 694
Section Heading: Time Series
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.
Answer: 92.3
Diff: 1 Page Ref: 694
Section Heading: Time Series
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
Section Heading: Time Series
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?
Answer: 115
Diff: 2 Page Ref: 694
Section Heading: Time Series
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.
Answer: Demand Forecast
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
Section Heading: Time Series
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?
Answer: 115
Diff: 1 Page Ref: 694
Section Heading: Time Series
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.
Answer: 119.9
Diff: 3 Page Ref: 697
Section Heading: Time Series
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
Section Heading: Time Series
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 ________.
Answer: 11
Diff: 1 Page Ref: 706
Section Heading: Forecast Accuracy
Keywords: forecast accuracy
AACSB: Analytic skills
63) If the forecast is 25 and the actual value is 25, then the error this period is ________.
Answer: 0
Diff: 1 Page Ref: 706
Section Heading: Forecast Accuracy
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
Section Heading: Time Series
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.
Answer: = -0.167
Diff: 2 Page Ref: 707
Section Heading: Forecast Accuracy
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
Answer: 1
Diff: 1 Page Ref: 706
Section Heading: Time Series
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?
Answer: 12
Diff: 2 Page Ref: 707
Section Heading: Forecast Accuracy
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
Section Heading: Time Series
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 |
Answer: MAD = 3
Diff: 2 Page Ref: 707
Section Heading: Forecast Accuracy
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.
Answer: F2009 = 21.1
Diff: 2 Page Ref: 696
Section Heading: Time Series
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
Section Heading: Time Series
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.
Answer:FApril =20.52, AFMay = 23.884
Diff: 3 Page Ref: 700
Section Heading: Time Series
Keywords: adjusted exponential smoothing method
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
Section Heading: Time Series
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
Section Heading: Time Series
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?
Answer: 0.15
Diff: 2 Page Ref: 697
Section Heading: Time Series
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?
Answer: 0.94117
Diff: 3 Page Ref: 716
Section Heading: Regression Models
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
Section Heading: Regression Models
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
Section Heading: Regression Models
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
Section Heading: Regression Models
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
Section Heading: Regression Models
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
Section Heading: Regression Models
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
Section Heading: Regression Models
Keywords: regression analysis, linear regression method
AACSB: Analytic skills
83) Calculate the coefficient of determination.
Answer: r2 = .93217
Diff: 2 Page Ref: 716
Section Heading: Regression Models
Keywords: correlation coefficient and the coefficient of determination
AACSB: Analytic skills
84) Calculate the correlation coefficient.
Answer: r = .96548
Diff: 2 Page Ref: 716
Section Heading: Regression Models
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
Section Heading: Regression Methods
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
Section Heading: Regression Methods
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
Section Heading: Regression Methods
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
Section Heading: Regression Methods
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
Section Heading: Regression Methods
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
Section Heading: Time Series Methods
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?
Answer: MAD = 4.67
Diff: 2 Page Ref: 706
Section Heading: Forecast Accuracy
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?
Answer: MSE = 27.33
Diff: 2 Page Ref: 708
Section Heading: Forecast Accuracy
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
Section Heading: Forecast Accuracy
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
Section Heading: Regression Models
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?
Answer: 392.4
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.
- A) seasonal pattern
- B) cycle
- C) trend
- D) prediction
Answer:
Diff: 1 Page Ref: 690
Section Heading: Forecasting Components
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.
- A) prediction
- B) seasonal pattern
- C) trend
- D) cyclical pattern
Answer:
Diff: 1 Page Ref: 690
Section Heading: Forecasting Components
Keywords: seasonal pattern
98) ________ methods are the most common type of forecasting method for the long-term strategic planning process.
- A) Regression
- B) Qualitative
- C) Time series
- D) Queuing
Answer:
Diff: 2 Page Ref: 691
Section Heading: Forecasting Components
Keywords: qualitative methods
99) ________ 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
Answer:
Diff: 2 Page Ref: 691
Section Heading: Forecasting Components
Keywords: time series analysis
100) ________ use management judgment, expertise, and opinion to make forecasts.
- A) Qualitative methods
- B) Regression
- C) Time series
- D) Quantitative methods
Answer:
Diff: 2 Page Ref: 691
Section Heading: Forecasting Components
Keywords: qualitative methods
101) 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
Answer:
Diff: 3 Page Ref: 693
Section Heading: Forecasting Components
Keywords: Delphi method
102) ________ has become increasingly crucial to compete in the modern international business environment.
- A) The Delphi method
- B) Technological forecasting
- C) Prediction
- D) Exponential smoothing
Answer:
Diff: 2 Page Ref: 693
Section Heading: Forecasting Components
Keywords: technological forecasting
103) 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) none of the above
Answer:
Diff: 2 Page Ref: 691
Section Heading: Forecasting Components
Keywords: forecasting components, trend, cyclical, seasonal
104) 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
Answer:
Diff: 2 Page Ref: 691
Section Heading: Forecasting Components
Keywords: forecasting components, trend, random, seasonal
105) 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
Answer:
Diff: 2 Page Ref: 691
Section Heading: Forecasting Components
Keywords: forecasting components, trend, seasonal, irregular
106) ________ 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
Answer:
Diff: 2 Page Ref: 695
Section Heading: Time Series Methods
Keywords: moving averages, time series analysis
107) ________ are good for stable demand with no pronounced behavioral patterns.
- A) Longer-period moving averages
- B) Shorter-period moving averages
- C) Moving averages
- D) Weighted moving averages
Answer:
Diff: 2 Page Ref: 693
Section Heading: Time Series Methods
Keywords: moving averages, time series analysis
108) ________ 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
Answer:
Diff: 2 Page Ref: 693
Section Heading: Time Series Methods
Keywords: time series analysis
109) 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
Answer:
Diff: 2 Page Ref: 697
Section Heading: Time Series Methods
Keywords: exponential smoothing
110) In adjusted exponential smoothing, the closer beta is to ________, the stronger a trend is reflected.
- A) -1 or 1
- B) -1
- C) 0
- D) 1
Answer:
Diff: 2 Page Ref: 700
Section Heading: Time Series Methods
Keywords: adjusted exponential smoothing
111) ________ is a linear regression model relating demand to time.
- A) Linear trend
- B) Linear regression
- C) Forecast demand
- D) Linear equation
Answer:
Diff: 2 Page Ref: 703
Section Heading: Time Series Methods
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?
- A) .01
- B) .50
- C) .90
- D) 3.14
Answer:
Diff: 2 Page Ref: 697
Section Heading: Time Series Methods
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?
- A) 36.9
- B) 57.5
- C) 60.5
- D) 62.5
Answer:
Diff: 2 Page Ref: 697
Section Heading: Time Series Methods
Keywords: simple exponential smoothing
AACSB: Analytic skills
114) ________ is the difference between the forecast and actual demand.
- A) Forecast mistake
- B) Forecast error
- C) MAD
- D) Forecast accuracy
Answer:
Diff: 2 Page Ref: 705
Section Heading: Forecast Accuracy
Keywords: forecast error, forecast accuracy
115) ________ is absolute error as a percentage of demand.
- A) Cumulative error
- B) MAD
- C) MAPD
- D) Average error
Answer:
Diff: 3 Page Ref: 707
Section Heading: Forecast Accuracy
Keywords: MAPD, forecast accuracy
116) ________ indicates a forecast is biased high.
- A) Large +
- B) Large –
- C) Large :
- D) Large x
Answer:
Diff: 2 Page Ref: 706
Section Heading: Forecast Accuracy
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.
- A) Correlation
- B) Linear regression
- C) Coefficient of determination
- D) Regression
Answer:
Diff: 2 Page Ref: 715
Section Heading: Regression Methods
Keywords: correlation, regression methods, linear regression model
118) ________ 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
Answer:
Diff: 2 Page Ref: 716
Section Heading: Regression Methods
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.
- A) dependent, dependent
- B) independent, dependent
- C) dependent, independent
- D) independent, independent
Answer:
Diff: 3 Page Ref: 716
Section Heading: Regression Methods
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?
- A) 19
- B) 20
- C) 21
- D) 22
Answer:
Diff: 2 Page Ref: 699
Section Heading: Forecast Accuracy
Keywords: forecast error, MAD
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.
- A) 227.5
- B) 275
- C) 280
- D) 290
Answer:
Diff: 2 Page Ref: 686
Section Heading: Time Series Methods
Keywords: moving average method
AACSB: Analytic skills
122) Use a 3-period moving average to forecast demand for period 7.
- A) 283.33
- B) 280
- C) 290
- D) 310
Answer:
Diff: 2 Page Ref: 686
Section Heading: Time Series Methods
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.
- A) 273
- B) 277
- C) 267.8
- D) 286.2
Answer:
Diff: 2 Page Ref: 689
Section Heading: Time Series Methods
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.)
- A) .20
- B) .22
- C) .26
- D) .30
Answer:
Diff: 2 Page Ref: 697-698
Section Heading: Forecasting Components
Keywords: seasonal factors
AACSB: Analytic skills
125) What is the seasonal index for the fourth quarter? (Round to the nearest hundredth.)
- A) .20
- B) .23
- C) .25
- D) .30
Answer:
Diff: 2 Page Ref: 697-698
Section Heading: Forecasting Components
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:
- A) 4575
- B) 4583
- C) 5668
- D) 6769
Answer:
Diff: 2 Page Ref: 697-698
Section Heading: Time Series Methods
Keywords: seasonal factors
AACSB: Analytic skills
127) 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
Answer:
Diff: 2 Page Ref: 699
Section Heading: Forecast Accuracy
Keywords: forecast error, MAD
128) 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
Answer:
Diff: 2 Page Ref: 698
Section Heading: Forecast Accuracy
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?
- A) 47.33
- B) 46.10
- C) 45.38
- D) 44.29
Answer:
Diff: 2 Page Ref: 694
Section Heading: Time Series Methods
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?
- A) 48.99
- B) 45.6
- C) 49.51
- D) 46.09
Answer:
Diff: 2 Page Ref: 696
Section Heading: Time Series Methods
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?
- A) 0.55
- B) -2.74
- C) 59.55
- D) 8.87
Answer:
Diff: 2 Page Ref: 716-719
Section Heading: Regression Methods
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?
- A) 41.25
- B) 40.64
- C) 43.16
- D) 42.88
Answer:
Diff: 2 Page Ref: 697
Section Heading: Time Series Methods
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?
- A) 0.92
- B) 0.86
- C) 0.80
- D) 0.71
Answer:
Diff: 2 Page Ref: 715
Section Heading: Regression Methods
Keywords: linear regression
AACSB: Analytic skills
Strayer MAT540 Week 5 Midterm exam
Mat 540 Quantitative Methods Midterm Exam Week 5
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Mat 540 Week 2 Homework Problems – Chapter 1 and Chapter 11
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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.
- For an annual volume of 12,000 tires, determine the total cost, total revenue, and profit.
- 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.
- What price should she charge for a hot dog in order to break even?
- What factors might occur during the season that would alter the volume sold and thus the
break-even price Annie might charge?
- 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.
- How many students does the college need to enroll in the first year to break even?
- If the college can enroll 75 students the first year, how much profit will it make?
- 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:
Grade Probability
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:
- 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.
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MAT 540 Chapter 14 Homework Problems
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- 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 Homework Chapter 15 Problems
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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 Homework Chapter 15 Problems
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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
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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.