Quantitative Analysis for Management, 11e (Render)
Chapter 1 Introduction to Quantitative Analysis
1) Interviews, statistical sampling, and company reports provide input data for quantitative analysis models.
Answer: TRUE
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
2) In the early 1900s, Henry Ford pioneered the principles of the scientific approach to management.
Answer: FALSE
Diff: 2
Topic: WHAT IS QUANTITATIVE ANALYSIS?
3) Managers do not need to be familiar with the limitations, assumptions, and/or specific applicability of the
quantitative analysis technique to use it for accurate decision making.
Answer: FALSE
Diff: 2
Topic: INTRODUCTION
4) During World War II, many new scientific and quantitative techniques were developed to assist the military,
and these developments were so successful that many companies started using similar techniques in managerial
decision making and planning after the war.
Answer: TRUE
Diff: 2
Topic: WHAT IS QUANTITATIVE ANALYSIS?
5) When a problem is difficult to quantify, it may be necessary to develop unspecific objectives.
Answer: FALSE
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
6) The Quantitative Analysis Approach consists of six steps.
Answer: FALSE
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
7) A mathematical model shows the relationship between quantifiable and non-quantifiable information.
Answer: FALSE
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
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8) Decision variables may also be called parameters.
Answer: FALSE
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
9) Model variables can be controllable or uncontrollable.
Answer: TRUE
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
10) A series of steps or procedures that are repeated is known as an algorithm.
Answer: TRUE
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
11) A model is a representation of a situation.
Answer: TRUE
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
12) A parameter is a measurable quantity that may vary or is subject to change.
Answer: FALSE
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
13) Trying various approaches and picking the one resulting in the best decision is called incomplete
enumeration.
Answer: FALSE
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
14) All problems can be solved by considering only the quantitative issues.
Answer: FALSE
Diff: 1
Topic: WHAT IS QUANTITATIVE ANALYSIS?
15) A profit equation is an example of a schematic model.
Answer: FALSE
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
16) Testing the data and model should be done before the results have been analyzed.
Answer: TRUE
Diff: 1
Topic: THE QUANTITATIVE ANALYSIS APPROACH
2
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17) Sensitivity analysis helps us estimate the effect of known and unknown errors in our model.
Answer: TRUE
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
18) Models can help us analyze a problem and sell a decision to those who must implement it.
Answer: TRUE
Diff: 1
Topic: HOW TO DEVELOP A QUANTITATIVE ANALYSIS MODEL
AACSB: Communication
19) A sensitivity analysis allows a manager to answer the "what if" questions.
Answer: TRUE
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
20) One problem in using a quantitative model is that the necessary data may be unavailable.
Answer: TRUE
Diff: 1
Topic: POSSIBLE PROBLEMS IN THE QUANTITATIVE ANALYSIS APPROACH
21) Which of the following terms is interchangeable with quantitative analysis?
A) management science
B) economics
C) financial analysis
D) statistics
E) None of the above
Answer: A
Diff: 1
Topic: WHAT IS QUANTITATIVE ANALYSIS?
22) Operations Research is known as
A) the science of numerical analysis.
B) the science of sensitivity analysis.
C) the science of better.
D) the science of modeling.
E) None of the above
Answer: C
Diff: 2
Topic: INTRODUCTION
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23) Who is credited with pioneering the principles of the scientific approach to management?
A) Adam Smith
B) Henri Fayol
C) John R. Locke
D) Frederick W. Taylor
E) Charles Babbage
Answer: D
Diff: 2
Topic: WHAT IS QUANTITATIVE ANALYSIS?
24) A(n) ________ is a representation of reality or a real-life situation.
A) objective
B) model
C) analysis
D) algorithm
E) None of the above
Answer: B
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
25) A measurable quantity that may vary, or is subject to change, and can be controlled is known as a(n)
A) decision variable.
B) algorithm.
C) parameter.
D) solution.
E) None of the above
Answer: A
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
26) A set of logical and mathematical operations performed in a specific sequence is called a(n)
A) complete enumeration.
B) diagnostic analysis.
C) algorithm.
D) objective.
E) None of the above
Answer: C
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
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27) The ability to examine the variability of a solution due to changes in the formulation of a problem is an
important part of the analysis of the results. This type of analysis is called ________ analysis.
A) sensitivity
B) implicit
C) normal
D) scale
E) objective
Answer: A
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
28) Which of the following is not one of the steps in the quantitative analysis approach?
A) Defining the Problem
B) Developing a Solution
C) Observing a hypothesis
D) Testing a Solution
E) Implementing the Results
Answer: C
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
29) The condition of improper data yielding misleading results is referred to as
A) garbage in, garbage out.
B) break-even point.
C) uncontrollable variable.
D) postoptimality.
E) None of the above
Answer: A
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
30) Expressing profits through the relationship among unit price, fixed costs, and variable costs is an example of
A) a sensitivity analysis model.
B) a quantitative analysis model.
C) a postoptimality relationship.
D) a parameter specification model.
E) None of the above
Answer: B
Diff: 1
Topic: HOW TO DEVELOP A QUANTITATIVE ANALYSIS MODEL
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31) The widespread applicability of operations research methods to business followed which war?
A) The U.S. Civil War
B) World War I
C) World War II
D) The Korean War
E) The Vietnam War
Answer: C
Diff: 2
Topic: WHAT IS QUANTITATIVE ANALYSIS?
32) Which of the following statement(s) are true regarding the advantages of mathematical modeling?
A) Models accurately represent reality.
B) Models can help decision makers formulate problems.
C) Models can save time.
D) Models may be the only way to solve some large and complex problems in a timely manner.
E) All of the above
Answer: E
Diff: 1
Topic: HOW TO DEVELOP A QUANTITATIVE ANALYSIS MODEL
33) A measurable quantity that is inherent in the problem is called a(n)
A) decision variable.
B) uncontrollable variable.
C) algorithm.
D) parameter.
E) enumeration variable.
Answer: D
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
34) Trying various approaches and picking the one that results in the best decision is called
A) the trial-and-error method.
B) incomplete enumeration.
C) complete enumeration.
D) algorithmic approximation.
E) sensitivity analysis.
Answer: A
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
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35) Models that do not involve risk or chance are
A) probabilistic models.
B) postoptimality models.
C) deterministic models.
D) MIS models.
E) None of the above
Answer: C
Diff: 2
Topic: HOW TO DEVELOP A QUANTITATIVE ANALYSIS MODEL
36) If input data are accurate to three significant digits, then the solution results can be accurate to how many
significant digits?
A) one
B) two
C) three
D) four
E) six
Answer: C
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
37) Postoptimality analysis is most closely associated with
A) collecting input data.
B) developing a model.
C) sensitivity analysis.
D) writing a computer program.
E) None of the above
Answer: C
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
38) The break-even point is an example of a
A) postoptimality model.
B) quantitative analysis model.
C) schematic model.
D) sensitivity analysis model.
E) None of the above
Answer: B
Diff: 1
Topic: HOW TO DEVELOP A QUANTITATIVE ANALYSIS MODEL
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39) Stochastic models are synonymous with
A) deterministic models
B) schematic models.
C) qualitative models.
D) conceptual models.
E) None of the above
Answer: E
Diff: 2
Topic: GLOSSARY
40) A controllable variable is also called a
A) parameter.
B) decision variable.
C) mathematical model.
D) measurable quantity.
E) None of the above
Answer: B
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
41) Evaluating all possible values of a variable in a model is called
A) trial and error.
B) complete enumeration.
C) an algorithm.
D) variablization.
E) None of the above
Answer: B
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
42) What is the formula for the break-even point of a simple profit model?
A) Fixed Cost / Variable Cost Per Unit
B) (Selling Price Per Unit —Variable Cost Per Unit) / Fixed Cost
C) Fixed Cost / (Selling Price Per Unit —Variable Cost Per Unit)
D) Fixed Cost / (Variable Cost Per Unit — Selling Price Per Unit)
E) Selling Price Per Unit — (Fixed Cost / Variable Cost Per Unit)
Answer: C
Diff: 2
Topic: HOW TO DEVELOP A QUANTITATIVE ANALYSIS MODEL
AACSB: Quantitative Skills
8
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43) The break-even point of a simple profit model represents a(n)
A) decision variable.
B) uncontrollable variable.
C) parameter.
D) constant.
E) None of the above
Answer: A
Diff: 3
Topic: HOW TO DEVELOP A QUANTITATIVE ANALYSIS MODEL
44) A(n) ________ model is one that is accurate and correctly represents the problem or system under
investigation.
A) robust
B) valid
C) sensitive
D) optimal
E) feasible
Answer: B
Diff: 2
Topic: HOW TO DEVELOP A QUANTITATIVE ANALYSIS MODEL
45) Which Excel feature is an optimization technique that can maximize or minimize a quantity given a set of
limitations or constraints?
A) Optimizer
B) Goal Seek
C) Analysis Tool-Pak
D) Algorithm Builder
E) Solver
Answer: E
Diff: 3
Topic: THE ROLE OF COMPUTERS AND SPREADSHEET MODELS IN THE QUANTITATIVE ANALYSIS
APPROACH
AACSB: Use of IT
46) Which Excel feature allows the user to specify a target or goal and the variable that is desired to change in
order to achieve that goal?
A) Solver
B) Goal Search
C) Target Search
D) Goal Seek
E) Target Seek
Answer: D
Diff: 3
Topic: THE ROLE OF COMPUTERS AND SPREADSHEET MODELS IN THE QUANTITATIVE ANALYSIS
APPROACH
9
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AACSB: Use of IT
47) All of the following are real computer applications that perform quantitative analysis except
A) Solver in Excel.
B) Goal Seek in Excel.
C) Excel QM.
D) POM-QM for Windows.
E) QA for Windows.
Answer: E
Diff: 2
Topic: THE ROLE OF COMPUTERS AND SPREADSHEET MODELS IN THE QUANTITATIVE ANALYSIS
APPROACH
AACSB: Use of IT
48) As one attempts to develop a model, which of the following problems might she encounter?
A) The problem may not fit a textbook approach.
B) There will be no data available to test the model.
C) Not everyone will understand the problem in the same way.
D) All of the above
E) None of the above
Answer: D
Diff: 1
Topic: POSSIBLE PROBLEMS IN THE QUANTITATIVE ANALYSIS APPROACH
49) Which of the following is a picture, drawing, or chart of reality?
A) scale model
B) physical model
C) mathematical model
D) schematic model
E) abstract model
Answer: D
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
50) Which of the following is not considered a possible problem in the quantitative analysis approach?
A) validity of the data
B) lack of commitment
C) resistance to change
D) subjective solutions
E) hard-to-understand mathematics
Answer: D
Diff: 2
Topic: POSSIBLE PROBLEMS IN THE QUANTITATIVE ANALYSIS APPROACH
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51) Quantitative analysis is ________.
Answer: the scientific approach to managerial decision making
Diff: 2
Topic: WHAT IS QUANTITATIVE ANALYSIS?
52) Identify the steps of the quantitative analysis approach.
Answer: (1) Defining the Problem, (2) Developing a Model, (3) Acquiring Input Data, (4) Developing a Solution,
(5) Testing the Solution, (6) Analyzing the Results, and (7) Implementing the Results
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
AACSB: Analytic Skills
53) A controllable variable is also called a ________ variable.
Answer: decision
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
54) A picture, drawing, or chart of reality is a ________ model
Answer: schematic
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
55) Identify some possible problems in the quantitative analysis approach.
Answer: Answers will vary but may include: conflicting viewpoints, ignoring the impact on other departments,
poor assumptions, outdated solutions, difficulty matching the textbook approach, trading off model complexity
with ease of understanding, poor input data, hard-to-understand mathematics, and having only one answer is
limiting.
Diff: 2
Topic: POSSIBLE PROBLEMS IN THE QUANTITATIVE ANALYSIS APPROACH
56) Identify three potential problems with people (two with management and one with the quantitative analysts
themselves) that may hinder successful implementation of a quantitative model.
Answer: Answers will vary but may include: (1) lack of commitment by management, (2) resistance to change by
management, and (3) lack of commitment by quantitative analysts.
Diff: 2
Topic: IMPLEMENTATION–NOT JUST THE FINAL STEP
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57) In making a decision, both ________ and quantitative factors must be considered.
Answer: qualitative
Diff: 2
Topic: WHAT IS QUANTITATIVE ANALYSIS?
58) Inaccurate model input data leads to inaccurate model solutions. This phenomenon is commonly referred to
as ________.
Answer: garbage in, garbage out
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
59) The solution process of ________ implies that we look at all possible solutions.
Answer: complete enumeration
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
60) Once we have a solution, we should then perform ________ analysis.
Answer: sensitivity or postoptimality
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
61) ________ models do not involve risk or chance.
Answer: Deterministic
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
62) ________ models are synonymous with stochastic models.
Answer: Probabilistic
Diff: 2
Topic: THE QUANTITATIVE ANALYSIS APPROACH
63) How can an analyst overcome the threats to successful implementation of a quantitative model?
Answer: Answers will vary; one solution is for analysts to work with users and take their feelings into account
instead of telling them what to do.
Diff: 2
Topic: IMPLEMENTATION–NOT JUST THE FINAL STEP
Quantitative Analysis for Management, 11e (Render)
Chapter 3 Decision Analysis
1) Expected monetary value (EMV) is the average or expected monetary outcome of a decision if it can be
repeated a large number of times.
Answer: TRUE
Diff: 2
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Topic: DECISION MAKING UNDER RISK
2) Expected monetary value (EMV) is the payoff you should expect to occur when you choose a particular
alternative.
Answer: FALSE
Diff: 2
Topic: DECISION MAKING UNDER RISK
3) The decision maker can control states of nature.
Answer: FALSE
Diff: 1
Topic: THE SIX STEPS IN DECISION MAKING
4) All decisions that result in a favorable outcome are considered to be good decisions.
Answer: FALSE
Diff: 2
Topic: INTRODUCTION
5) The difference in decision making under risk and decision making under uncertainty is that under risk, we
think we know the probabilities of the states of nature, while under uncertainty we do not know the probabilities
of the states of nature.
Answer: TRUE
Diff: 2
Topic: TYPES OF DECISION-MAKING ENVIRONMENTS
6) EVPI (expected value of perfect information) is a measure of the maximum EMV as a result of additional
information.
Answer: TRUE
Diff: 2
Topic: DECISION MAKING UNDER RISK
7) When using the EOL as a decision criterion, the best decision is the alternative with the largest EOL value.
Answer: FALSE
Diff: 2
Topic: DECISION MAKING UNDER RISK
8) To determine the effect of input changes on decision results, we should perform a sensitivity analysis.
Answer: TRUE
Diff: 2
Topic: DECISION MAKING UNDER RISK
9) The maximax decision criterion is used by pessimistic decision makers and maximizes the maximum outcome
for every alternative.
Answer: FALSE
Diff: 1
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Topic: DECISION MAKING UNDER UNCERTAINTY
10) The maximin decision criterion is used by pessimistic decision makers and minimizes the maximum outcome
for every alternative.
Answer: FALSE
Diff: 2
Topic: DECISION MAKING UNDER UNCERTAINTY
11) Optimistic decision makers tend to discount favorable outcomes.
Answer: FALSE
Diff: 2
Topic: THE SIX STEPS IN DECISION MAKING
12) The decision theory processes of maximizing expected monetary value (EMV) and minimizing expected
opportunity loss (EOL) should lead us to choose the same alternatives.
Answer: TRUE
Diff: 2
Topic: DECISION MAKING UNDER RISK
13) The several criteria (maximax, maximin, equally likely, criterion of realism, minimax regret) used for decision
making under uncertainty may lead to the choice of different alternatives.
Answer: TRUE
Diff: 1
Topic: DECISION MAKING UNDER UNCERTAINTY
14) A decision table is sometimes called a payout table.
Answer: TRUE
Diff: 2
Topic: THE SIX STEPS IN DECISION MAKING
15) The nodes on decision trees represent either decisions or states of nature.
Answer: TRUE
Diff: 2
Topic: DECISION TREES
16) Any problem that can be presented in a decision table can also be graphically portrayed in a decision tree.
Answer: TRUE
Diff: 2
Topic: DECISION TREES
17) Any problem that can be represented in a decision tree can be easily portrayed in a decision table.
Answer: FALSE
Diff: 2
Topic: DECISION TREES
14
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18) In a decision table, all of the alternatives are listed down the left side of the table, while all of the possible
outcomes or states of nature are listed across the top.
Answer: TRUE
Diff: 2
Topic: THE SIX STEPS IN DECISION MAKING
19) The EMV approach and Utility theory always result in the same choice of alternatives.
Answer: FALSE
Diff: 1
Topic: UTILITY THEORY
20) Utility theory may help the decision maker include the impact of qualitative factors that are difficult to
include in the EMV model.
Answer: TRUE
Diff: 1
Topic: UTILITY THEORY
21) In a decision problem where we wish to use Bayes' theorem to calculate posterior probabilities, we should
always begin our analysis with the assumption that all states of nature are equally likely, and use the sample
information to revise these probabilities to more realistic values.
Answer: FALSE
Diff: 2
Topic: HOW PROBABILITY VALUES ARE ESTIMATED BY BAYESIAN ANALYSIS
22) A utility curve that shows utility increasing at an increasing rate as the monetary value increases represents
the utility curve of a risk seeker.
Answer: TRUE
Diff: 2
Topic: UTILITY THEORY
23) A utility curve that shows utility increasing at a decreasing rate as the monetary value increases represents the
utility curve of a risk seeker.
Answer: FALSE
Diff: 2
Topic: UTILITY THEORY
24) The criterion of realism is also called the Laplace criterion.
Answer: FALSE
Diff: 2
Topic: DECISION MAKING UNDER UNCERTAINTY
25) Utility values typically range from -1 to +1.
Answer: FALSE
Diff: 2
Topic: UTILITY THEORY
15
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16
Copyright © 2012 Pearson Education, Inc. publishing as Prentice Hall
26) By studying a person's Utility Curve, one can determine whether the individual is a risk seeker, risk avoider,
or is indifferent to risk.
Answer: TRUE
Diff: 2
Topic: UTILITY THEORY
27) The equally likely decision criterion is also called the Laplace criterion.
Answer: TRUE
Diff: 2
Topic: DECISION MAKING UNDER UNCERTAINTY
28) Utility theory provides a decision criterion that is superior to the EMV or EOL in that it may allow the
decision maker to incorporate her own attitudes toward risk.
Answer: TRUE
Diff: 2
Topic: UTILITY THEORY
29) The assignment of a utility value of 1 to an alternative implies that alternative is preferred to all others.
Answer: TRUE
Diff: 2
Topic: UTILITY THEORY
30) A second table (an opportunity loss table) must be computed when applying the maximin decision criterion.
Answer: FALSE
Diff: 2
Topic: DECISION MAKING UNDER UNCERTAINTY
31) The following figure illustrates a utility curve for someone who is a risk seeker.
Answer: TRUE
Diff: 2
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Topic: UTILITY THEORY
18
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32) An analytic and systematic approach to the study of decision making is referred to as
A) decision making under risk.
B) decision making under uncertainty.
C) decision theory.
D) decision analysis.
E) decision making under certainty.
Answer: C
Diff: 2
Topic: INTRODUCTION
33) What makes the difference between good decisions and bad decisions?
A) A good decision is based on logic.
B) A good decision considers all available data.
C) A good decision considers all alternatives.
D) A good decision applies quantitative approaches.
E) All the above
Answer: C
Diff: 1
Topic: INTRODUCTION
34) Expected monetary value (EMV) is
A) the average or expected monetary outcome of a decision if it can be repeated a large number of times.
B) the average or expected value of the decision, if you know what would happen ahead of time.
C) the average or expected value of information if it were completely accurate.
D) the amount you would lose by not picking the best alternative.
E) a decision criterion that places an equal weight on all states of nature.
Answer: A
Diff: 2
Topic: DECISION MAKING UNDER RISK
35) Which of the following is not considered a criteria for decision making under uncertainty?
A) optimistic
B) pessimistic
C) equally likely
D) random selection
E) minimax regret
Answer: D
Diff: 1
Topic: DECISION MAKING UNDER UNCERTAINTY
36) A pessimistic decision making criterion is
A) maximax.
B) equally likely.
C) maximin.
D) decision making under certainty.
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E) minimax regret.
Answer: C
Diff: 2
Topic: DECISION MAKING UNDER UNCERTAINTY
37) Which of the following is true about the expected value of perfect information?
A) It is the amount you would pay for any sample study.
B) It is calculated as EMV minus EOL.
C) It is calculated as expected value with perfect information minus maximum EMV.
D) It is the amount charged for marketing research.
E) None of the above
Answer: C
Diff: 2
Topic: DECISION MAKING UNDER RISK
38) Which of the following is not a characteristic of a good decision?
A) based on logic
B) considers all available data
C) considers all possible alternatives
D) employs appropriate quantitative techniques
E) always results in a favorable outcome
Answer: E
Diff: 2
Topic: INTRODUCTION
39) The following is a payoff table giving profits for various situations.
What decision would an optimist make?
A) Alternative 1
B) Alternative 2
C) Alternative 3
D) Do Nothing
E) State of Nature A
Answer: B
Diff: 2
Topic: DECISION MAKING UNDER UNCERTAINTY
AACSB: Analytic Skills
20
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40) The following is a payoff table giving profits for various situations.
What decision would a pessimist make?
A) Alternative 1
B) Alternative 2
C) Alternative 3
D) Do Nothing
E) State of Nature A
Answer: A
Diff: 2
Topic: DECISION MAKING UNDER UNCERTAINTY
AACSB: Analytic Skills
41) The following is an opportunity loss table.
What decision should be made based on the minimax regret criterion?
A) Alternative 1
B) Alternative 2
C) Alternative 3
D) State of Nature A
E) Does not matter
Answer: C
Diff: 2
Topic: DECISION MAKING UNDER UNCERTAINTY
AACSB: Analytic Skills
21
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42) The following is an opportunity loss table.
What decision should be made based on the minimax regret criterion?
A) Alternative 1
B) Alternative 2
C) Alternative 3
D) State of Nature C
E) Does not matter
Answer: B
Diff: 2
Topic: DECISION MAKING UNDER UNCERTAINTY
AACSB: Analytic Skills
43) The following is a payoff table.
What decision should be made based on the minimax regret criterion?
A) Alternative 1
B) Alternative 2
C) Alternative 3
D) State of Nature C
E) Does not matter
Answer: A
Diff: 2
Topic: DECISION MAKING UNDER UNCERTAINTY
AACSB: Analytic Skills
22
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44) The following is a payoff table.
What decision should be made based on the minimax regret criterion?
A) Alternative 1
B) Alternative 2
C) Alternative 3
D) State of Nature C
E) Does not matter
Answer: A
Diff: 2
Topic: DECISION MAKING UNDER UNCERTAINTY
AACSB: Analytic Skills
45) The following is an opportunity-loss table.
The probabilities for the states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively. If a person were to use the
expected opportunity loss criterion, what decision would be made?
A) Alternative 1
B) Alternative 2
C) Alternative 3
D) State of Nature C
E) State of Nature B
Answer: C
Diff: 2
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
23
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46) The following is a payoff table giving profits for various situations.
The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively. If a person selected Alternative
1, what would the expected profit be?
A) 120
B) 133.33
C) 126
D) 180
E) None of the above
Answer: C
Diff: 2
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
47) Dr. Mac, a surgeon, must decide what mode of treatment to use on Mr. Samuels. There are three modes of
treatment: Mode A, B, and C; and three possible states of nature: 1.Treatment succeeds and patient leads a normal
life, 2. Patient survives treatment but is permanently disabled, and 3. Patient fails to survive treatment. Dr. Mac
has prepared the decision table below. What mode of treatment maximizes the expected value?
A) Mode A
B) Mode B
C) Mode C
D) All three treatments are equally desirable.
E) Normal Life
Answer: C
Diff: 2
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
24
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48) Consider the following payoff table.
Based upon these probabilities, a person would select Alternative 2. Suppose there is concern about the accuracy
of these probabilities. It can be stated that Alternative 2 will remain the best alternative as long as the probability
of A is at least
A) 0.33.
B) 0.50.
C) 0.40.
D) 0.60.
E) None of the above
Answer: A
Diff: 2
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
49) Consider the following payoff table.
How much should be paid for a perfect forecast of the state of nature?
A) 170
B) 30
C) 10
D) 100
E) 40
Answer: B
Diff: 2
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
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50) The following is a payoff table giving profits for various situations.
The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively. If a perfect forecast of the
future were available, what is the expected value with this perfect information?
A) 130
B) 160
C) 166
D) 36
E) None of the above
Answer: C
Diff: 2
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
51) The following is a payoff table giving profits for various situations.
The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively. If a perfect forecast of the
future were available, what is the expected value of perfect information (EVPI)?
A) 166
B) 0
C) 36
D) 40
E) None of the above
Answer: C
Diff: 3
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
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52) Nick has plans to open some pizza restaurants, but he is not sure how many to open. He has prepared a
payoff table to help analyze the situation.
As Nick does not know how his product will be received, he assumes that all three states of nature are equally
likely to occur. If he uses the equally likely criterion, what decision would he make?
A) Open 1
B) Open 2
C) Good market
D) Fair market
E) Do nothing
Answer: B
Diff: 2
Topic: DECISION MAKING UNDER UNCERTAINTY
AACSB: Analytic Skills
53) Nick has plans to open some pizza restaurants, but he is not sure how many to open. He has prepared a
payoff table to help analyze the situation.
Nick believes there is a 40 percent chance that the market will be good, a 30 percent chance that it will be fair, and
a 30 percent chance that it will be poor. A market research firm will analyze market conditions and will provide a
perfect forecast (they provide a money back guarantee). What is the most that should be paid for this forecast?
A) $ 44,000
B) $ 53,000
C) $123,000
D) $176,000
E) $132,000
Answer: C
Diff: 2
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
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54) Which of the following is the fourth step of the "Six Steps in Decision Making"?
A) Select one of the mathematical decision theory models.
B) List the possible alternatives.
C) Apply the model and make your decision.
D) List the payoff or profit of each combination of alternatives and outcomes.
E) Identify the possible outcomes or states of nature.
Answer: D
Diff: 2
Topic: THE SIX STEPS IN DECISION MAKING
55) Which of the following is not one of the steps considered in the "Six Steps in Decision Making"?
A) Clearly define the problem at hand
B) List the possible alternatives.
C) Apply the model and make your decision.
D) List the payoff or profit of each combination of alternatives and outcomes.
E) Evaluate the success of the decision.
Answer: E
Diff: 2
Topic: THE SIX STEPS IN DECISION MAKING
56) Optimistic decision makers tend to ________.
A) magnify favorable outcomes
B) ignore bad outcomes
C) discount favorable outcomes
D) A and B
E) B and C
Answer: D
Diff: 2
Topic: THE SIX STEPS IN DECISION MAKING
AACSB: Reflective Thinking
57) Pessimistic decision makers tend to ________.
A) magnify favorable outcomes
B) ignore bad outcomes
C) discount favorable outcomes
D) A and B
E) B and C
Answer: C
Diff: 2
Topic: THE SIX STEPS IN DECISION MAKING
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58) In decision theory, we call the payoffs resulting from each possible combination of alternatives and outcomes
________.
A) marginal values
B) conditional values
C) conditional probabilities
D) Bayesian values
E) joint values
Answer: B
Diff: 2
Topic: THE SIX STEPS IN DECISION MAKING
59) Another name for a decision table is a ________.
A) payment table
B) payout table
C) payoff table
D) pay-up table
E) decision tree
Answer: C
Diff: 1
Topic: THE SIX STEPS IN DECISION MAKING
60) How are decision tables organized?
A) alternatives down the left, states of nature on top, payoffs inside
B) states of nature down the left, alternatives on top, payoffs inside
C) alternatives down the left, payoffs on top, states of nature inside
D) payoffs down the left, alternatives on top, states of nature inside
E) states of nature down the left, payoffs on top, alternatives inside
Answer: A
Diff: 1
Topic: THE SIX STEPS IN DECISION MAKING
61) The three decision-making environments are decision making under ________.
A) utility, risk, and certainty
B) utility, risk, and uncertainty
C) utility, certainty, and uncertainty
D) utility, equity, and certainty
E) risk, certainty, and uncertainty
Answer: E
Diff: 1
Topic: TYPES OF DECISION-MAKING ENVIRONMENTS
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62) In decision making under ________, there are several possible outcomes for each alternative, and the decision
maker does not know the probabilities of the various outcomes.
A) risk
B) utility
C) certainty
D) probability
E) uncertainty
Answer: E
Diff: 2
Topic: TYPES OF DECISION-MAKING ENVIRONMENTS
63) In decision making under ________, there are several possible outcomes for each alternative, and the decision
maker knows the probability of occurrence of each outcome.
A) risk
B) utility
C) certainty
D) probability
E) uncertainty
Answer: A
Diff: 2
Topic: TYPES OF DECISION-MAKING ENVIRONMENTS
64) The optimistic decision criterion is the criterion of ________.
A) maximax
B) maximin
C) realism
D) equally likely
E) minimax regret
Answer: A
Diff: 2
Topic: DECISION MAKING UNDER UNCERTAINTY
65) The Hurwicz criterion is also called the criterion of ________.
A) regret
B) equality
C) optimism
D) realism
E) pessimism
Answer: D
Diff: 2
Topic: DECISION MAKING UNDER UNCERTAINTY
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66) The equally likely criterion is also called the ________ criterion.
A) Hurwicz
B) uncertainty
C) Laplace
D) LaFlore
E) Huchenmeizer
Answer: C
Diff: 2
Topic: DECISION MAKING UNDER UNCERTAINTY
67) Decision trees are particularly useful when
A) perfect information is available.
B) formulating a conditional values table.
C) the opportunity loss table is available.
D) a sequence of decisions must be made.
E) all possible outcomes and alternatives are not known.
Answer: D
Diff: 2
Topic: DECISION TREES
68) The expected value of sample information (EVSI) can be used to
A) establish a maximum amount to spend on additional information.
B) calculate conditional probabilities.
C) establish risk avoidance.
D) provide points on a utility curve.
E) None of the above
Answer: A
Diff: 2
Topic: DECISION MAKING UNDER RISK
69) A market research survey is available for $10,000. Using a decision tree analysis, it is found that the expected
monetary value with no survey is $62,000. If the expected value of sample information is -$7,000, what is the
expected monetary value with the survey?
A) $45,000
B) $62,000
C) -$17,000
D) $55,000
E) None of the above
Answer: A
Diff: 2
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
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70) A market research survey is available for $10,000. Using a decision tree analysis, it is found that the expected
monetary value with the survey is $75,000. The expected monetary value with no survey is $62,000. What is the
expected value of sample information?
A) -$7,000
B) $3,000
C) $7,000
D) $13,000
E) None of the above
Answer: E
Diff: 2
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
71) In the construction of decision trees, which of the following shapes represents a state of nature node?
A) square
B) circle
C) diamond
D) triangle
E) None of the above
Answer: B
Diff: 1
Topic: DECISION MAKING UNDER RISK
72) In the construction of decision trees, which of the following shapes represents a decision node?
A) square
B) circle
C) diamond
D) triangle
E) None of the above
Answer: A
Diff: 1
Topic: DECISION MAKING UNDER RISK
73) Bayes' theorem enables decision makers to revise probabilities based on
A) perfect information.
B) knowing, ahead of time, the actual outcome of the decision.
C) additional information.
D) measurements of utility.
E) None of the above
Answer: C
Diff: 2
Topic: HOW PROBABILITY VALUES ARE ESTIMATED BY BAYESIAN ANALYSIS
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74) In Bayesian analysis, conditional probabilities are also known as which of the following?
A) anterior probabilities
B) posterior probabilities
C) prior probabilities
D) marginal probabilities
E) joint probabilities
Answer: B
Diff: 2
Topic: HOW PROBABILITY VALUES ARE ESTIMATED BY BAYESIAN ANALYSIS
75) A company is considering producing a new children's bar soap. A market research firm has told the company
that if they perform a survey, a positive survey of a favorable market occurs 65 percent of the time. That is,
P(positive survey ∣ favorable market) = 0.65. Similarly, 40 percent of the time the survey falsely predicts a
favorable market; thus, P(positive survey ∣ unfavorable market) = 0.40. These statistics indicate the accuracy of the
survey. Prior to contacting the market research firm, the company's best estimate of a favorable market was 50
percent. So, P(favorable market) = 0.50 and P(unfavorable market) = 0.50. Using Bayes' theorem, determine the
probability of a favorable market given a favorable survey.
A) 0.62
B) 0.38
C) 0.53
D) 0.65
E) None of the above
Answer: A
Diff: 2
Topic: HOW PROBABILITY VALUES ARE ESTIMATED BY BAYESIAN ANALYSIS
AACSB: Analytic Skills
76) The Hurwicz criterion coefficient of realism measures the decision maker's degree of ________.
A) utility
B) pessimism
C) certainty
D) optimism
E) regret
Answer: D
Diff: 2
Topic: DECISION MAKING UNDER UNCERTAINTY
77) What is the range of the Hurwicz criterion coefficient of realism α?
A) 1 to 100
B) 1 to 10
C) 0 to 10
D) 0 to 1
E) −1 to 1
Answer: D
Diff: 2
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Topic: DECISION MAKING UNDER UNCERTAINTY
78) Utilization of Bayes' theorem requires the use of all but
A) prior probabilities.
B) marginal probabilities.
C) conditional probabilities.
D) posterior probabilities.
E) expected monetary values (EMV).
Answer: E
Diff: 2
Topic: HOW PROBABILITY VALUES ARE ESTIMATED BY BAYESIAN ANALYSIS
79) A risk avoider is a person for whom the utility of an outcome
A) decreases as the monetary value increases.
B) stays the same as monetary value increases.
C) increases at an increasing rate as the monetary value increases.
D) increases at a decreasing rate as monetary value increases.
E) None of the above
Answer: D
Diff: 2
Topic: UTILITY THEORY
80) A utility curve showing utility increasing at an increasing rate as the monetary value increases represents
A) a risk avoider.
B) utility assessment.
C) a risk seeker.
D) conditional values.
E) expected utilities.
Answer: C
Diff: 2
Topic: UTILITY THEORY
81) In constructing a utility curve,
A) a comparison is made of the different amounts of money at different times.
B) the certainty of a certain amount is compared with the willingness to gamble that amount on a larger amount.
C) one takes the risk out of gambling.
D) inflation plays a critical part in the evaluation.
E) None of the above
Answer: B
Diff: 2
Topic: UTILITY THEORY
82) Utility values typically range from
A) -1 to 1
B) 1 to 10
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C) 0 to 1
D) 1 to 100
E) None of the above
Answer: C
Diff: 2
Topic: UTILITY THEORY
83) A rational decision maker must choose between two alternatives. Alternative 1 has a higher EMV than
Alternative 2, but the decision maker chooses Alternative 2. What might explain why this occurs?
A) Alternative 2 may have a higher expected utility.
B) Alternative 1 may have a lower expected opportunity loss.
C) The probabilities are not known.
D) A rational decision maker could not possibly choose alternative 2.
E) None of the above
Answer: A
Diff: 2
Topic: UTILITY THEORY
AACSB: Reflective Thinking
84) Robert Weed is considering purchasing life insurance. He must pay a $180 premium for a $100,000 life
insurance policy. If he dies this year, his beneficiary will receive $100,000. If he does not die this year, the
insurance company pays nothing and Robert must consider paying another premium next year. Based on
actuarial tables, there is a 0.001 probability that Robert will die this year. If Robert wishes to maximize his EMV,
he would not buy the policy if the EMV were negative for him. He has determined that the EMV is, negative for
him, but decides to purchase the insurance anyway. Why?
A) He believes that the actual likelihood of his death occurring in the next twelve months is really much greater
than the actuarial estimate.
B) While the EMV is negative, the utility gained from purchasing the insurance is positive, and high.
C) Mr. Weed is not rational.
D) A or C
E) None of the above
Answer: B
Diff: 2
Topic: UTILITY THEORY
AACSB: Reflective Thinking
85) If one's utility curve is not a straight line (i.e., risk indifferent), then one's utility can, over a particular range of
EMV,
A) increase at an increasing rate as the monetary value increases.
B) increase at an increasing rate as the monetary value decreases.
C) increase at a decreasing rate as the monetary value increases.
D) increase at a decreasing rate as the monetary value decreases.
E) Any of the above
Answer: E
Diff: 2
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Topic: UTILITY THEORY
86) It is sometimes said that "Those who gamble the most are the ones who can least afford to lose." These people
gamble because
A) the EMV is positive.
B) the EMV is negative.
C) the gambler has no family to consider if he/she dies.
D) there is utility other than monetary to consider.
E) None of the above
Answer: D
Diff: 2
Topic: UTILITY THEORY
87) A manager is deciding whether or not to build a small facility. Demand is uncertain and can be either at a
high or low level. If the manager chooses a small facility and demand is low, the payoff is $300. If the manager
chooses a small facility and demand is high, the payoff is $100. On the other hand, if the manager chooses a large
facility and demand is low, the payoff is -$200, but if demand is high, the payoff is $800.
(a)
What would be the best decision based on the maximax criterion?
(b)
What would be the best decision based on the maximin criterion?
(c)
What would be the best decision based on the minimax regret?
Answer:
(a) large facility highest overall payoff = $800
(b) small facility highest minimum potential payoff = $100
(c) large facility lowest maximum regret = $500
Diff: 1
Topic: DECISION MAKING UNDER UNCERTAINTY
AACSB: Analytic Skills
88) A manager is deciding whether or not to build a small facility. Demand is uncertain and can be either at a
high or low level. If the manager chooses a small facility and demand is low, the payoff is $100. If the manager
chooses a small facility and demand is high, the payoff is $300. On the other hand, if the manager chooses a large
facility and demand is low, the payoff is -$200, but if demand is high, the payoff is $800.
(a)
What would be the best decision based on the Laplace criterion?
(b)
What would be the best decision based on Hurwicz's criterion of realism using α = 0.6?
Answer:
(a) large facility equally weighted payoff = $300
(b) large facility weighted average = $400
Diff: 1
Topic: DECISION MAKING UNDER UNCERTAINTY
AACSB: Analytic Skills
89) A concessionaire for the local ballpark has developed a table of conditional values for the various alternatives
(stocking decision) and states of nature (size of crowd).
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If the probabilities associated with the states of nature are 0.30 for a large crowd, 0.50 for an average crowd, and
0.20 for a small crowd, determine:
(a)
the alternative that provides the greatest expected monetary value (EMV)
(b)
the expected value of perfect information (EVPI)
Answer:
(a) For large inventory alternative maximum EMV = $12,200
(b) EVPI = 13800 -12200 = 1,600
Diff: 2
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
90) A concessionaire for the local ballpark has developed a table of conditional values for the various alternatives
(stocking decision) and states of nature (size of crowd).
If the probabilities associated with the states of nature are 0.30 for a large crowd, 0.50 for an average crowd, and
0.20 for a small crowd, determine:
(a)
the opportunity loss table.
(b)
minimum expected opportunity loss (EOL).
Answer:
(a)
Opportunity loss table
(b)
minimum EOL = $1,600
Diff: 2
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
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91) The ABC Co. is considering a new consumer product. They believe there is a probability of 0.4 that the XYZ
Co. will come out with a competitive product. If ABC adds an assembly line for the product and XYZ does not
follow with a competitive product, their expected profit is $40,000; if they add an assembly line and XYZ does
follow, they still expect a $10,000 profit. If ABC adds a new plant addition and XYZ does not produce a
competitive product, they expect a profit of $600,000; if XYZ does compete for this market, ABC expects a loss of
$100,000.
(a)
Determine the EMV of each decision.
(b)
Determine the EOL of each decision.
(c)
Compare the results of (a) and (b).
(d)
Calculate the EVPI.
Answer:
(a)
(b)
(c)
The plant addition is best for both models. The maximum EMV alternative is always the same as the
minimum EOL alternative.
(d)
EVPI = 44,000
Diff: 2
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
92) The ABC Co. is considering a new consumer product. They have no idea whether or not the XYZ Co. will
come out with a competitive product. If ABC adds an assembly line for the product and XYZ does not follow
with a competitive product, their expected profit is $40,000; if they add an assembly line and XYZ does follow,
they still expect a $10,000 profit. If ABC adds a new plant addition and XYZ does not produce a competitive
product, they expect a profit of $600,000; if XYZ does compete for this market, ABC expects a loss of $100,000.
Calculate Hurwicz's criterion of realism using α's of a. 0.7, b. 0.3, and c. 0.1.
Answer:
Diff: 2
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Topic: DECISION MAKING UNDER UNCERTAINTY
AACSB: Analytic Skill 93) Barbour Electric is considering the introduction of a new product. This product can be
produced in one of several ways: (a) using the present assembly line at a cost of $25 per unit, (b) using the
current assembly line after it has been overhauled (at a cost of $10,000) with a cost of $22 per unit; and (c) on an
entirely new assembly line (costing $30,000) designed especially for the new product with a per unit cost of $20.
Barbour is worried, however, about the impact of competition. If no competition occurs, they expect to sell 15,000
units the first year. With competition, the number of units sold is expected to drop to 9,000. At the moment, their
best estimate is that there is a 40% chance of competition. They have decided to make their decision based on the
first year sales.
(a)
Develop the decision table (EMV).
(b)
Develop a decision table (EOL).
(c)
What should they do?
Answer:
(a)
(b)
(c)
They should build the new line.
Diff: 2
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
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94) The following payoff table provides profits based on various possible decision alternatives and various levels
of demand.
The probability of a low demand is 0.4, while the probability of a medium and high demand is each 0.3.
(a)
What decision would an optimist make?
(b)
What decision would a pessimist make?
(c)
What is the highest possible expected monetary value?
(d)
Calculate the expected value of perfect information for this situation.
Answer:
(a)
Alternative 3
(b)
Alternative 2
(c)
Alternative 1 maximum EMV = 110
(d)
EVPI = 117- 110 = 7
Diff: 2
Topic: DECISION MAKING UNDER UNCERTAINTY and DECISION MAKING UNDER RISK
AACSB: Analytic Skills
95) The ABC Co. is considering a new consumer product. They believe that the XYZ Co. may come out with a
competing product. If ABC adds an assembly line for the product and XYZ does not follow with a competitive
product, their expected profit is $40,000; if they add an assembly line and XYZ does follow, they still expect a
$10,000 profit. If ABC adds a new plant addition and XYZ does not produce a competitive product, they expect a
profit of $600,000; if XYZ does compete for this market, ABC expects a loss of $100,000. For what value of
probability that XYZ will offer a competing product will ABC be indifferent between the alternatives?
Answer: Let X = probability XYZ offers a competing product. Then:
EMV(assembly line) = $10,000∗X + $40,000∗(1-X)
EMV(addition) = -$100,000∗X + $600,000∗(1-X) or:
$10,000∗X + $40,000∗(1-X) = -$100,000*X + $600,000∗(1-X) or:
$10,000∗X - $40,000∗X + $40,000 = -$100,000∗X -$600,000∗X + $600,000
-$30,000∗X + $700,000∗X = $600,000 - $40,000
$670,000∗X = $560,000
X = $560,000/$670,000 = 0.836
If the probability that XYZ will offer a competing product is estimated to be 0.836, then ABC will be indifferent
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between the two alternatives. If the probability that XYZ will offer a competing product is estimated to be less
than 0.836, then ABC should invest in the addition.
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Diff: 2
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
96) A company is considering expansion of its current facility to meet increasing demand. A major expansion
would cost $500,000, while a minor expansion would cost $200,000. If demand is high in the future, the major
expansion would result in an additional profit of $800,000, but if demand is low, then there would be a loss of
$500,000. If demand is high, the minor expansion will result in an increase in profits of $200,000, but if demand is
low, then there is a loss of $100,000. The company has the option of not expanding. For what probability of a
high demand will the company be indifferent between the two expansion alternatives?
Answer:
If we define X = probability of high demand, then:
$300,000∗X - $1,000,000∗(1-X) = $0∗X - $300,000∗(1-X)
X = 0.7
For a probability of high demand equal to 0.7, the decision maker would be indifferent between the two
expansion alternatives.
Diff: 2
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
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97) Orders for clothing from a particular manufacturer for this year's Christmas shopping season must be placed
in February. The cost per unit for a particular dress is $20 while the anticipated selling price is $50. Demand is
projected to be 50, 60, or 70 units. There is a 40 percent chance that demand will be 50 units, a 50 percent chance
that demand will be 60 units, and a 10 percent chance that demand will be 70 units. The company believes that
any leftover goods will have to be scrapped. How many units should be ordered in February?
Answer: Payoff Table:
EMV(50) = .4(1500) + .5(1500) + .1(1500) = 1500
EMV(60) = .4(1300) + .5(1800) + .1(1800) = 1600
EMV(70) = .4(1100) + .5(1600) + .1(2100) = 1450
Thus, 60 units should be ordered.
Diff: 2
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
98) Suppose that the payoff from an investment depends upon market conditions. A great market has payoff of
$200,000, a normal market has a payoff of $100,000, and a poor market has a payoff of $20,000. Using an α-value
of 0.3, what is the criterion of realism value?
Answer: 0.3($200,000) + 0.7($20,000) = $74,000
Diff: 1
Topic: DECISION MAKING UNDER UNCERTAINTY
AACSB: Analytic Skills
99) A market research survey is available for $5,000. Using a decision tree analysis, it is found that the expected
monetary value with no survey is $49,000. If the expected value of sample information is -$4,000, what is the
expected monetary value with the survey?
Answer: EV with SI = 49,000 - $4,000 + 5,000 = $50,000
Diff: 1
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
100) David N. Goliath is planning to open a sporting goods store. However, the initial investment is $120,000. He
currently has this money in a certificate of deposit earning 10 percent. He may leave it there if he decides not to
open the store. If he opens the store and it is successful he will generate a profit of $50,000. If it is not successful,
he will lose $90,000. What would the probability of a successful store have to be for David to prefer this to
investing in a CD?
Answer: p(50,000) - (1-p)(90,000) > 0.10(120,000), therefore p > 0.7286
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Diff: 2
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
101) You are considering adding a new food product to your store for resale. You are certain that, in a month,
minimum demand for the product will be 6 units, while maximum demand will be 8 units. (Unfortunately, the
new product has a one-month shelf life and is considered to be waste at the end of the month.) You will pay
$60/unit for this new product while you plan to sell the product at a $40/unit profit. The estimated demand for
this new product in any given month is 6 units(p=0.1), 7 units(p=0.4), and 8 units(p=0.5). Using EMV analysis,
how many units of the new product should be purchased for resale?
Answer: EMV(purchase 6 for resale) = 6(40)(0.1) + 6(40)(0.4) + 6(40)(0.5) = 240
EMV(purchase 7 for resale) = [6(40)-60](0.1) + 7(40)(0.4) + 7(40)(0.5) = 270
EMV(purchase 8 for resale) = [6(40)-2(60)](0.1) + [7(40)-60](0.4) + 8(40)(0.5) = 260
Choose to purchase 7 units for resale (largest EMV)
Diff: 2
Topic: DECISION MAKING UNDER RISK
AACSB: Analytic Skills
102) Mark M. Upp has just been fired as the university bookstore manager for setting prices too low (only 20
percent above suggested retail). He is considering opening a competing bookstore near the campus, and he has
begun an analysis of the situation. There are two possible sites under consideration. One is relatively small,
while the other is large. If he opens at Site 1 and demand is good, he will generate a profit of $50,000. If demand
is low, he will lose $10,000. If he opens at Site 2 and demand is high, he will generate a profit of $80,000, but he
will lose $30,000 if demand is low. He also has the option of not opening at either site. He believes that there is a
50 percent chance that demand will be high. A market research study will cost $5,000. The probability of a good
demand given a favorable study is 0.8. The probability of a good demand given an unfavorable study is 0.1.
There is a 60 percent chance that the study will be favorable.
(a)
Should Mark use the study? Why?
(b)
If the study is done and the results are favorable, what would Mark's expected profit be?
Answer:
(a)
Yes, he should use the study. His EMV with the study is $29,800 while the highest EMV without the
study is $25,000.
(b)
Given a favorable survey result, Mark would select Site 2 and have an EMV of $53,000.
Diff: 2
Topic: DECISION TREES
AACSB: Analytic Skills
44
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103) Mark M. Upp has just been fired as the university bookstore manager for setting prices too low (only 20
percent above suggested retail). He is considering opening a competing bookstore near the campus, and he has
begun an analysis of the situation. There are two possible sites under consideration. One is relatively small,
while the other is large. If he opens at Site 1 and demand is good, he will generate a profit of $50,000. If demand
is low, he will lose $10,000. If he opens at Site 2 and demand is high, he will generate a profit of $80,000, but he
will lose $30,000 if demand is low. He also has the option of not opening either. He believes that there is a 50
percent chance that demand will be high. Mark can purchase a market research study. The probability of a good
demand given a favorable study is 0.8. The probability of a good demand given an unfavorable study is 0.1.
There is a 60 percent chance that the study will be favorable. Should Mark use the study? Why? What is the
maximum amount Mark should be willing to pay for this study? What is the maximum amount he should pay
for any study?
Answer: Yes, he should use the study. His EMV with the study is $34,800 while the highest EMV without the
study is $25,000. He should pay no more than $9,800 for this study. He should pay no more than $10,000 for a
"perfect" study.
Diff: 2
Topic: DECISION TREES
AACSB: Analytic Skills
104) Before a marketing research study was done, John Colorado believed there was a 50/50 chance that his music
store would be a success. The research team determined that there is a 0.9 probability that the marketing research
will be favorable given a successful music store. There is also a 0.8 probability that the marketing research will be
unfavorable given an unsuccessful music store.
(a)
If the marketing research is favorable, what is the revised probability of a successful music store?
(b)
If the marketing research is unfavorable, what is the revised probability of a successful music store?
Answer:
(a)
0.82
(b)
0.11
Diff: 2
Topic: HOW PROBABILITY VALUES ARE ESTIMATED BY BAYESIAN ANALYSIS
AACSB: Analytic Skills
105) Before a market survey is done, there is a 50/50 chance that a new soccer supply store would be a success.
The people doing the survey have determined that there is a 0.9 probability that the survey will be favorable
given a successful store. There is also a 0.75 probability that the survey will be unfavorable given an unsuccessful
store. What is the probability that the survey will be unfavorable?
Answer: (1−.9)(.5) + (.75)(.5) = 0.425
Diff: 2
Topic: HOW PROBABILITY VALUES ARE ESTIMATED BY BAYESIAN ANALYSIS
AACSB: Analytic Skills
45
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106) Before a marketing research study was done, John Colorado believed there was a 50/50 chance that his music
store would be a success. The research team determined that there is a 0.9 probability that the marketing research
will be favorable given a successful music store. There is also a 0.8 probability that the marketing research will be
unfavorable given an unsuccessful music store.
(a) If the marketing research is favorable, what is the revised probability of an unsuccessful music store?
(b) If the marketing research is unfavorable, what is the revised probability of an unsuccessful music store?
Answer: (a) 0.18
(b) 0.89
Diff: 2
Topic: HOW PROBABILITY VALUES ARE ESTIMATED BY BAYESIAN ANALYSIS
AACSB: Analytic Skills
107) Mark M. Upp has just been fired as the university bookstore manager for setting prices too low (only 20
percent above suggested retail). He is considering opening a competing bookstore near the campus, and he has
begun an analysis of the situation. There are two possible sites under consideration. One is relatively small while
the other is large. If he opens at Site 1 and demand is good, he will generate a profit of $50,000. If demand is low,
he will lose $10,000. If he opens at Site 2 and demand is high he will generate a profit of $80,000, but he will lose
$30,000 if demand is low. He also has decided that he will open at one of these sites. He believes that there is a 60
percent chance that demand will be high. He assigns the following utilities to the different profits:
Using expected utility theory, what should Mark do?
Answer: Expected utility (Site 1) = 0.6(0.72) + 0.4(0.22) = 0.52
Expected utility (Site 2) = 0.6(1.00) + 0.4(0.00) = 0.60
Therefore he should open at Site 2.
Diff: 2
Topic: UTILITY THEORY
AACSB: Analytic Skills
46
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108) Mark M. Upp has just been fired as the university book store manager for setting prices too low (only 20
percent above suggested retail). He is considering opening a competing bookstore near the campus, and he has
begun an analysis of the situation. There are two possible sites under consideration. One is relatively small,
while the other is large. If he opens at Site 1 and demand is good, he will generate a profit of $50,000. If demand
is low, he will lose $10,000. If he opens at Site 2 and demand is high he will generate a profit of $80,000, but he
will lose $30,000 if demand is low. He also has decided that he will open at one of these sites. He believes that
there is a 50 percent chance that demand will be high. He assigns the following utilities to the different profits:
For what value of utility for $50,000, U(50000), will Mark be indifferent between the two alternatives?
Answer: Expected utility (Site 1) = 0.5X + 0.5(0.22)
Expected utility (Site 2) = 0.5(1) + 0.5(0) = 0.50
Therefore: 0.5X + 0.5(0.22) = 0.50
or: 0.5X = 0.50 - 0.11 = 0.39
and:
X = 0.39/0.5 = 0.78
Therefore, if Mark has U(50,000) = 0.78 he will be indifferent between the two alternatives.
Diff: 2
Topic: UTILITY THEORY
AACSB: Analytic Skills
109) Suppose that the payoff from an investment depends upon market conditions. A great market has payoff of
$200,000, a normal market has a payoff of $100,000, and a poor market has a payoff of $20,000. What is the
Laplace criterion value?
Answer: ($200,000 + $100,000 + $20,000) / 3 = $320,000/3 = $106,667
Diff: 1
Topic: DECISION MAKING UNDER UNCERTAINTY
AACSB: Analytic Skills
110) Briefly describe decision making under certainty.
Answer: Decision makers know with certainty of the consequence of every alternative or decision choice.
Diff: 2
Topic: TYPES OF DECISION-MAKING ENVIRONMENTS
111) Briefly describe decision making under risk.
Answer: There are several possible outcomes for each alternative, and the decision maker knows the probability
of occurrence of each outcome.
Diff: 2
Topic: TYPES OF DECISION-MAKING ENVIRONMENTS
112) Briefly describe decision making under uncertainty.
Answer: There are several possible outcomes for each alternative, and the decision maker does not know the
probabilities of the various outcomes.
Diff: 2
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Topic: TYPES OF DECISION-MAKING ENVIRONMENTS
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113) List the six steps in decision making.
Answer: 1.
Clearly define the problem at hand.
2.
List the possible alternatives.
3.
Identify the possible outcomes or states of nature.
4.
List the payoff or profit of each combination of alternatives and outcomes.
5.
Select one of the mathematical decision theory models.
6.
Apply the model and make your decision.
Diff: 2
Topic: THE SIX STEPS IN DECISION MAKING
114) Describe the structure of a payoff table.
Answer: All of the alternatives are listed down the left side of the table, and all of the possible outcomes or states
of nature are listed across the top. The body of the table contains the actual payoffs.
Diff: 2
Topic: THE SIX STEPS IN DECISION MAKING
115) Briefly describe decision tree analysis.
Answer: define the problem, draw the tree, assign the probabilities to the states of nature, estimate payoffs for
each alternative, compute EMV
Diff: 2
Topic: DECISION TREES
116) Briefly describe EVSI.
Answer: EVSI = EMV (best decision with sample information) - EMV (of best decision without sample
information)
Diff: 2
Topic: DECISION TREES
117) Describe the utility curve of a risk seeker.
Answer: utility increasing at an increasing rate as the monetary value increases
Diff: 2
Topic: UTILITY THEORY
118) Describe the utility curve of a risk avoider.
Answer: utility increasing at a decreasing rate as the monetary value increases
Diff: 2
Topic: UTILITY THEORY
119) List the five major decision criteria used when making decisions under uncertainty.
Answer: (1) maximax (optimistic), (2) maximin (pessimistic), (3) criterion of realism (Hurwicz), (4) equally likely
(Laplace), and (5) minimax regret
Diff: 2
Topic: DECISION MAKING UNDER UNCERTAINTY
49
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Quantitative Analysis for Management, 11e (Render)
Chapter 7 Linear Programming Models: Graphical and Computer Methods
1) Management resources that need control include machinery usage, labor volume, money spent, time used,
warehouse space used, and material usage.
Answer: TRUE
Diff: 1
Topic: INTRODUCTION
2) In the term linear programming, the word programming comes from the phrase "computer programming."
Answer: FALSE
Diff: 2
Topic: INTRODUCTION
3) One of the assumptions of LP is "simultaneity."
Answer: FALSE
Diff: 2
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
4) Any linear programming problem can be solved using the graphical solution procedure.
Answer: FALSE
Diff: 1
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
5) An LP formulation typically requires finding the maximum value of an objective while simultaneously
maximizing usage of the resource constraints.
Answer: FALSE
Diff: 2
Topic: FORMULATING LP PROBLEMS
6) There are no limitations on the number of constraints or variables that can be graphed to solve an LP problem.
Answer: FALSE
Diff: 1
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
7) Resource restrictions are called constraints.
Answer: TRUE
Diff: 1
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
8) One of the assumptions of LP is "proportionality."
Answer: TRUE
Diff: 2
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
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9) The set of solution points that satisfies all of a linear programming problem's constraints simultaneously is
defined as the feasible region in graphical linear programming.
Answer: TRUE
Diff: 2
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
10) An objective function is necessary in a maximization problem but is not required in a minimization problem.
Answer: FALSE
Diff: 1
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
11) In some instances, an infeasible solution may be the optimum found by the corner point method.
Answer: FALSE
Diff: 2
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
12) The rationality assumption implies that solutions need not be in whole numbers (integers).
Answer: FALSE
Diff: 2
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
13) The solution to a linear programming problem must always lie on a constraint.
Answer: TRUE
Diff: 2
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
14) In a linear program, the constraints must be linear, but the objective function may be nonlinear.
Answer: FALSE
Diff: 2
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
15) Resource mix problems use LP to decide how much of each product to make, given a series of resource
restrictions.
Answer: FALSE
Diff: 2
Topic: FORMULATING LP PROBLEMS
16) The existence of non-negativity constraints in a two-variable linear program implies that we are always
working in the northwest quadrant of a graph.
Answer: FALSE
Diff: 2
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
17) In linear programming terminology, "dual price" and "sensitivity price" are synonyms.
Answer: FALSE
51
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Diff: 2
Topic: SENSITIVITY ANALYSIS
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18) Any time that we have an isoprofit line that is parallel to a constraint, we have the possibility of multiple
solutions.
Answer: TRUE
Diff: 2
Topic: FOUR SPECIAL CASES IN LP
19) If the isoprofit line is not parallel to a constraint, then the solution must be unique.
Answer: TRUE
Diff: 2
Topic: FOUR SPECIAL CASES IN LP
AACSB: Reflective Thinking
20) When two or more constraints conflict with one another, we have a condition called unboundedness.
Answer: FALSE
Diff: 2
Topic: FOUR SPECIAL CASES IN LP
21) The addition of a redundant constraint lowers the isoprofit line.
Answer: FALSE
Diff: 2
Topic: FOUR SPECIAL CASES IN LP
22) Sensitivity analysis enables us to look at the effects of changing the coefficients in the objective function, one at
a time.
Answer: TRUE
Diff: 2
Topic: SENSITIVITY ANALYSIS
23) A widely used mathematical programming technique designed to help managers and decision making
relative to resource allocation is called ________.
A) linear programming
B) computer programming
C) constraint programming
D) goal programming
E) None of the above
Answer: A
Diff: 1
Topic: INTRODUCTION
24) Typical resources of an organization include ________.
A) machinery usage
B) labor volume
C) warehouse space utilization
D) raw material usage
E) All of the above
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Answer: E
Diff: 1
Topic: INTRODUCTION
54
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25) Which of the following is not a property of all linear programming problems?
A) the presence of restrictions
B) optimization of some objective
C) a computer program
D) alternate courses of action to choose from
E) usage of only linear equations and inequalities
Answer: C
Diff: 2
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
26) A feasible solution to a linear programming problem
A) must be a corner point of the feasible region.
B) must satisfy all of the problem's constraints simultaneously.
C) need not satisfy all of the constraints, only the non-negativity constraints.
D) must give the maximum possible profit.
E) must give the minimum possible cost.
Answer: B
Diff: 2
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
27) Infeasibility in a linear programming problem occurs when
A) there is an infinite solution.
B) a constraint is redundant.
C) more than one solution is optimal.
D) the feasible region is unbounded.
E) there is no solution that satisfies all the constraints given.
Answer: E
Diff: 2
Topic: FOUR SPECIAL CASES IN LP
28) In a maximization problem, when one or more of the solution variables and the profit can be made infinitely
large without violating any constraints, the linear program has
A) an infeasible solution.
B) an unbounded solution.
C) a redundant constraint.
D) alternate optimal solutions.
E) None of the above
Answer: B
Diff: 2
Topic: FOUR SPECIAL CASES IN LP
29) Which of the following is not a part of every linear programming problem formulation?
A) an objective function
B) a set of constraints
C) non-negativity constraints
55
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D) a redundant constraint
E) maximization or minimization of a linear function
Answer: D
Diff: 2
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
30) When appropriate, the optimal solution to a maximization linear programming problem can be found by
graphing the feasible region and
A) finding the profit at every corner point of the feasible region to see which one gives the highest value.
B) moving the isoprofit lines towards the origin in a parallel fashion until the last point in the feasible region is
encountered.
C) locating the point that is highest on the graph.
D) None of the above
E) All of the above
Answer: A
Diff: 2
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
31) The mathematical theory behind linear programming states that an optimal solution to any problem will lie at
a(n) ________ of the feasible region.
A) interior point or center
B) maximum point or minimum point
C) corner point or extreme point
D) interior point or extreme point
E) None of the above
Answer: C
Diff: 1
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
32) Which of the following is not a property of linear programs?
A) one objective function
B) at least two separate feasible regions
C) alternative courses of action
D) one or more constraints
E) objective function and constraints are linear
Answer: B
Diff: 1
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
33) The corner point solution method
A) will always provide one, and only one, optimum.
B) will yield different results from the isoprofit line solution method.
C) requires that the profit from all corners of the feasible region be compared.
D) requires that all corners created by all constraints be compared.
E) will not provide a solution at an intersection or corner where a non-negativity constraint is involved.
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Answer: C
Diff: 2
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
57
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34) When a constraint line bounding a feasible region has the same slope as an isoprofit line,
A) there may be more than one optimum solution.
B) the problem involves redundancy.
C) an error has been made in the problem formulation.
D) a condition of infeasibility exists.
E) None of the above
Answer: A
Diff: 2
Topic: FOUR SPECIAL CASES IN LP
35) The simultaneous equation method is
A) an alternative to the corner point method.
B) useful only in minimization methods.
C) an algebraic means for solving the intersection of two or more constraint equations.
D) useful only when more than two product variables exist in a product mix problem.
E) None of the above
Answer: C
Diff: 2
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
36) Consider the following linear programming problem:
The maximum possible value for the objective function is
A) 360.
B) 480.
C) 1520.
D) 1560.
E) None of the above
Answer: C
Diff: 3
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
58
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37) Consider the following linear programming problem:
The feasible corner points are (48,84), (0,120), (0,0), (90,0). What is the maximum possible value for the objective
function?
A) 1032
B) 1200
C) 360
D) 1600
E) None of the above
Answer: B
Diff: 2
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
38) Consider the following linear programming problem:
Which of the following points (X,Y) is not a feasible corner point?
A) (0,60)
B) (105,0)
C) (120,0)
D) (100,10)
E) None of the above
Answer: C
Diff: 2
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
59
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39) Consider the following linear programming problem:
Which of the following points (X,Y) is not feasible?
A) (50,40)
B) (20,50)
C) (60,30)
D) (90,10)
E) None of the above
Answer: A
Diff: 2
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
40) Two models of a product — Regular (X) and Deluxe (Y) — are produced by a company. A linear
programming model is used to determine the production schedule. The formulation is as follows:
The optimal solution is X = 100, Y = 0.
How many units of the regular model would be produced based on this solution?
A) 0
B) 100
C) 50
D) 120
E) None of the above
Answer: B
Diff: 1
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
60
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41) Two models of a product — Regular (X) and Deluxe (Y) — are produced by a company. A linear
programming model is used to determine the production schedule. The formulation is as follows:
The optimal solution is X=100, Y=0.
Which of these constraints is redundant?
A) the first constraint
B) the second constraint
C) the third constraint
D) All of the above
E) None of the above
Answer: B
Diff: 3
Topic: FOUR SPECIAL CASES IN LP
AACSB: Analytic Skills
42) Consider the following linear programming problem:
What is the optimum solution to this problem (X,Y)?
A) (0,0)
B) (50,0)
C) (0,100)
D) (400,0)
E) None of the above
Answer: B
Diff: 3
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
61
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43) Consider the following linear programming problem:
This is a special case of a linear programming problem in which
A) there is no feasible solution.
B) there is a redundant constraint.
C) there are multiple optimal solutions.
D) this cannot be solved graphically.
E) None of the above
Answer: E
Diff: 3
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
44) Consider the following linear programming problem:
This is a special case of a linear programming problem in which
A) there is no feasible solution.
B) there is a redundant constraint.
C) there are multiple optimal solutions.
D) this cannot be solved graphically.
E) None of the above
Answer: A
Diff: 3
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
62
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45) Which of the following is not acceptable as a constraint in a linear programming problem (maximization)?
A) Constraint 1
B) Constraint 2
C) Constraint 3
D) Constraint 4
E) None of the above
Answer: A
Diff: 2
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
46) If one changes the contribution rates in the objective function of an LP,
A) the feasible region will change.
B) the slope of the isoprofit or isocost line will change.
C) the optimal solution to the LP is sure to no longer be optimal.
D) All of the above
E) None of the above
Answer: B
Diff: 2
Topic: SENSITIVITY ANALYSIS
47) Sensitivity analysis may also be called
A) postoptimality analysis.
B) parametric programming.
C) optimality analysis.
D) All of the above
E) None of the above
Answer: D
Diff: 2
Topic: SENSITIVITY ANALYSIS
48) Sensitivity analyses are used to examine the effects of changes in
A) contribution rates for each variable.
B) technological coefficients.
C) available resources.
D) All of the above
E) None of the above
Answer: D
Diff: 2
Topic: SENSITIVITY ANALYSIS
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49) Which of the following is a basic assumption of linear programming?
A) The condition of uncertainty exists.
B) Independence exists for the activities.
C) Proportionality exists in the objective function and constraints.
D) Divisibility does not exist, allowing only integer solutions.
E) Solutions or variables may take values from -∞ to +∞.
Answer: C
Diff: 2
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
50) The condition when there is no solution that satisfies all the constraints simultaneously is called
A) boundedness.
B) redundancy.
C) optimality.
D) dependency.
E) None of the above
Answer: E
Diff: 2
Topic: FOUR SPECIAL CASES IN LP
51) If the addition of a constraint to a linear programming problem does not change the solution, the constraint is
said to be
A) unbounded.
B) non-negative.
C) infeasible.
D) redundant.
E) bounded.
Answer: D
Diff: 2
Topic: FOUR SPECIAL CASES IN LP
52) Which of the following is not an assumption of LP?
A) simultaneity
B) certainty
C) proportionality
D) divisibility
E) additivity
Answer: A
Diff: 2
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
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53) The difference between the left-hand side and right-hand side of a less-than-or-equal-to constraint is referred
to as
A) surplus.
B) constraint.
C) slack.
D) shadow price.
E) None of the above
Answer: C
Diff: 2
Topic: LINEAR PROGRAMMING MODELS: GRAPHICAL AND COMPUTER METHODS
54) The difference between the left-hand side and right-hand side of a greater-than-or-equal-to constraint is
referred to as
A) surplus.
B) constraint.
C) slack.
D) shadow price.
E) None of the above
Answer: A
Diff: 2
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
55) A constraint with zero slack or surplus is called a
A) nonbinding constraint.
B) resource constraint.
C) binding constraint.
D) nonlinear constraint.
E) linear constraint.
Answer: C
Diff: 1
Topic: SOLVING FLAIR FURNITURE’S LP PROBLEM USING QM FOR WINDOWS AND EXCEL
56) A constraint with positive slack or surplus is called a
A) nonbinding constraint.
B) resource constraint.
C) binding constraint.
D) nonlinear constraint.
E) linear constraint.
Answer: A
Diff: 1
Topic: SOLVING FLAIR FURNITURE’S LP PROBLEM USING QM FOR WINDOWS AND EXCEL
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57) The increase in the objective function value that results from a one-unit increase in the right-hand side of that
constraint is called
A) surplus.
B) shadow price.
C) slack.
D) dual price.
E) None of the above
Answer: B
Diff: 2
Topic: SENSITIVITY ANALYSIS
58) A straight line representing all non-negative combinations of X1 and X2 for a particular profit level is called
a(n)
A) constraint line.
B) objective line.
C) sensitivity line.
D) profit line.
E) isoprofit line.
Answer: E
Diff: 2
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
59) In order for a linear programming problem to have a unique solution, the solution must exist
A) at the intersection of the non-negativity constraints.
B) at the intersection of a non-negativity constraint and a resource constraint.
C) at the intersection of the objective function and a constraint.
D) at the intersection of two or more constraints.
E) None of the above
Answer: D
Diff: 2
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
60) In order for a linear programming problem to have multiple solutions, the solution must exist
A) at the intersection of the non-negativity constraints.
B) on a non-redundant constraint parallel to the objective function.
C) at the intersection of the objective function and a constraint.
D) at the intersection of three or more constraints.
E) None of the above
Answer: B
Diff: 2
Topic: FOUR SPECIAL CASES IN LP
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61) Consider the following linear programming problem:
The maximum possible value for the objective function is
A) 360.
B) 480.
C) 1520.
D) 1560.
E) None of the above
Answer: E
Diff: 3
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
62) Consider the following linear programming problem:
Which of the following points (X,Y) is feasible?
A) (10,120)
B) (120,10)
C) (30,100)
D) (60,90)
E) None of the above
Answer: C
Diff: 2
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
67
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63) Consider the following linear programming problem:
Which of the following points (X,Y) is in the feasible region?
A) (30,60)
B) (105,5)
C) (0,210)
D) (100,10)
E) None of the above
Answer: D
Diff: 2
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
64) Consider the following linear programming problem:
Which of the following points (X,Y) is feasible?
A) (50,40)
B) (30,50)
C) (60,30)
D) (90,20)
E) None of the above
Answer: C
Diff: 2
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
65) Which of the following is not an assumption of LP?
A) certainty
B) proportionality
C) divisibility
D) multiplicativity
E) additivity
Answer: D
Diff: 2
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
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66) Consider the following linear programming problem:
This is a special case of a linear programming problem in which
A) there is no feasible solution.
B) there is a redundant constraint.
C) there are multiple optimal solutions.
D) this cannot be solved graphically.
E) None of the above
Answer: B
Diff: 3
Topic: FOUR SPECIAL CASES IN LP
AACSB: Analytic Skills
67) Which of the following functions is not linear?
A) 5X + 3Z
B) 3X + 4Y + Z - 3
C) 2X + 5YZ
D) Z
E) 2X - 5Y + 2Z
Answer: C
Diff: 1
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
68) Which of the following is not one of the steps in formulating a linear program?
A) Graph the constraints to determine the feasible region.
B) Define the decision variables.
C) Use the decision variables to write mathematical expressions for the objective function and the constraints.
D) Identify the objective and the constraints.
E) Completely understand the managerial problem being faced.
Answer: A
Diff: 2
Topic: FORMULATING LP PROBLEMS
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69) Which of the following is not acceptable as a constraint in a linear programming problem (minimization)?
A) Constraint 1
B) Constraint 2
C) Constraint 3
D) Constraint 4
E) Constraint 5
Answer: E
Diff: 2
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
70) What type of problems use LP to decide how much of each product to make, given a series of resource
restrictions?
A) resource mix
B) resource restriction
C) product restriction
D) resource allocation
E) product mix
Answer: E
Diff: 2
Topic: FORMULATING LP PROBLEMS
71) Consider the following linear programming problem:
This is a special case of a linear programming problem in which
A) there is no feasible solution.
B) there is a redundant constraint.
C) there are multiple optimal solutions.
D) this cannot be solved graphically.
E) None of the above
Answer: B
Diff: 3
Topic: FOUR SPECIAL CASES IN LP
AACSB: Analytic Skills
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72) Consider the following constraints from a linear programming problem:
2X + Y ≤ 200
X + 2Y ≤ 200
X, Y ≥ 0
If these are the only constraints, which of the following points (X,Y) cannot be the optimal solution?
A) (0, 0)
B) (0, 200)
C) (0,100)
D) (100, 0)
E) (66.67, 66.67)
Answer: B
Diff: 3
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
73) Consider the following constraints from a linear programming problem:
2X + Y ≤ 200
X + 2Y ≤ 200
X, Y ≥ 0
If these are the only constraints, which of the following points (X,Y) cannot be the optimal solution?
A) (0, 0)
B) (0, 100)
C) (65, 65)
D) (100, 0)
E) (66.67, 66.67)
Answer: C
Diff: 3
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
74) A furniture company is producing two types of furniture. Product A requires 8 board feet of wood and 2 lbs
of wicker. Product B requires 6 board feet of wood and 6 lbs of wicker. There are 2000 board feet of wood
available for product and 1000 lbs of wicker. Product A earns a profit margin of $30 a unit and Product B earns a
profit margin of $40 a unit. Formulate the problem as a linear program.
Answer:
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Diff: 2
Topic: FORMULATING LP PROBLEMS
AACSB: Analytic Skills
75) As a supervisor of a production department, you must decide the daily production totals of a certain product
that has two models, the Deluxe and the Special. The profit on the Deluxe model is $12 per unit and the Special's
profit is $10. Each model goes through two phases in the production process, and there are only 100 hours
available daily at the construction stage and only 80 hours available at the finishing and inspection stage. Each
Deluxe model requires 20 minutes of construction time and 10 minutes of finishing and inspection time. Each
Special model requires 15 minutes of construction time and 15 minutes of finishing and inspection time. The
company has also decided that the Special model must comprise at least 40 percent of the production total.
(a)
Formulate this as a linear programming problem.
(b)
Find the solution that gives the maximum profit.
Answer:
(b) Optimal solution: X1 = 120, X2 = 240
Profit = $3,840
Diff: 3
Topic: FORMULATING LP PROBLEMS and GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
72
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76) The Fido Dog Food Company wishes to introduce a new brand of dog biscuits (composed of chicken and
liver-flavored biscuits) that meets certain nutritional requirements. The liver-flavored biscuits contain 1 unit of
nutrient A and 2 units of nutrient B, while the chicken-flavored ones contain 1 unit of nutrient A and 4 units of
nutrient B. According to federal requirements, there must be at least 40 units of nutrient A and 60 units of
nutrient B in a package of the new biscuit mix. In addition, the company has decided that there can be no more
than 15 liver-flavored biscuits in a package. If it costs 1 cent to make a liver-flavored biscuit and 2 cents to make a
chicken-flavored one, what is the optimal product mix for a package of the biscuits in order to minimize the firm's
cost?
(a)
Formulate this as a linear programming problem.
(b)
Find the optimal solution for this problem graphically.
(c)
Are any constraints redundant? If so, which one or ones?
(d)
What is the total cost of a package of dog biscuits using the optimal mix?
Answer:
(b) Corner points (0,40) and (15,25)
Optimal solution is (15,25) with cost of 65.
(c) 2X1 + 4X2 ≥ 60 is redundant.
(d) minimum cost = 65 cents
Diff: 3
Topic: FORMULATING LP PROBLEMS and GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
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77) Consider the following linear program:
(a)
Solve the problem graphically. Is there more than one optimal solution? Explain.
(b)
Are there any redundant constraints?
Answer:
(a) Corner points (0,50), (0,200), (50,50), (75,75), (50,150)
Optimum solutions: (75,75) and (50,150). Both yield a profit of $3,000.
(b) The constraint X1 ≤ 100 is redundant since 3X1 + X2 ≤ 300 also means that X1 cannot exceed 100.
Diff: 3
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
78) Solve the following linear programming problem using the corner point method:
Answer: Feasible corner points (X,Y): (0,3) (0,10) (2.4,8.8) (6.75,3)
Maximum profit 70.5 at (6.75,3).
Diff: 3
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
79) Solve the following linear programming problem using the corner point method:
Answer: Feasible corner points (X,Y): (0,2) (0,10) (4,8) (10,2)
Maximum profit is 52 at (4,8).
Diff: 3
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
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80) Billy Penny is trying to determine how many units of two types of lawn mowers to produce each day. One of
these is the Standard model, while the other is the Deluxe model. The profit per unit on the Standard model is
$60, while the profit per unit on the Deluxe model is $40. The Standard model requires 20 minutes of assembly
time, while the Deluxe model requires 35 minutes of assembly time. The Standard model requires 10 minutes of
inspection time, while the Deluxe model requires 15 minutes of inspection time. The company must fill an order
for 6 Deluxe models. There are 450 minutes of assembly time and 180 minutes of inspection time available each
day. How many units of each product should be manufactured to maximize profits?
Answer:
Maximum profit is $780 by producing 9 Standard and 6 Deluxe models.
Diff: 3
Topic: FORMULATING LP PROBLEMS and GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
81) Two advertising media are being considered for promotion of a product. Radio ads cost $400 each, while
newspaper ads cost $600 each. The total budget is $7,200 per week. The total number of ads should be at least 15,
with at least 2 of each type. Each newspaper ad reaches 6,000 people, while each radio ad reaches 2,000 people.
The company wishes to reach as many people as possible while meeting all the constraints stated. How many ads
of each type should be placed?
Answer:
Feasible corner points (R,N): (9,6) (13,2) (15,2)
Maximum exposure 54,000 with 9 radio and 6 newspaper ads.
Diff: 3
Topic: FORMULATING LP PROBLEMS and GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
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82) Suppose a linear programming (minimization) problem has been solved and the optimal value of the objective
function is $300. Suppose an additional constraint is added to this problem. Explain how this might affect each of
the following:
(a) the feasible region,
(b) the optimal value of the objective function.
Answer:
(a) Adding a new constraint will reduce the size of the feasible region unless it is a redundant constraint. It can
never make the feasible region any larger. However, it could make the problem infeasible.
(b) A new constraint can only reduce the size of the feasible region; therefore, the value of the objective function
will either increase or remain the same. If the original solution is still feasible, it will remain the optimal solution.
Diff: 2
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM and FOUR SPECIAL CASES IN LP
AACSB: Analytic Skills
83) Upon retirement, Mr. Klaws started to make two types of children's wooden toys in his shop Wuns and
Toos. Wuns yield a variable profit of $9 each and Toos have a contribution margin of $8 each. Even though his
electric saw overheats, he can make 7 Wuns or 14 Toos each day. Since he doesn't have equipment for drying the
lacquer finish he puts on the toys, the drying operation limits him to 16 Wuns or 8 Toos per day.
(a)
Solve this problem using the corner point method.
(b)
For what profit ratios would the optimum solution remain the optimum solution?
Answer:
Corner points (0,0), (7,0), (0,8), (4,6)
Optimum profit $84 at (4,6).
Diff: 3
Topic: FORMULATING LP PROBLEMS and GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
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84) Susanna Nanna is the production manager for a furniture manufacturing company. The company produces
tables (X) and chairs (Y). Each table generates a profit of $80 and requires 3 hours of assembly time and 4 hours
of finishing time. Each chair generates $50 of profit and requires 3 hours of assembly time and 2 hours of
finishing time. There are 360 hours of assembly time and 240 hours of finishing time available each month. The
following linear programming problem represents this situation.
Maximize
Subject to:
80X + 50Y
3X + 3Y ≤ 360
4X + 2Y ≤ 240
X, Y ≥ 0
The optimal solution is X = 0, and Y = 120.
(a)
What would the maximum possible profit be?
(b)
How many hours of assembly time would be used to maximize profit?
(c)
If a new constraint, 2X + 2Y ≤ 400, were added, what would happen to the maximum possible profit?
Answer:
(a) 6000, (b) 360, (c) It would not change.
Diff: 3
Topic: FORMULATING LP PROBLEMS and GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
85) As a supervisor of a production department, you must decide the daily production totals of a certain product
that has two models, the Deluxe and the Special. The profit on the Deluxe model is $12 per unit, and the Special's
profit is $10. Each model goes through two phases in the production process, and there are only 100 hours
available daily at the construction stage and only 80 hours available at the finishing and inspection stage. Each
Deluxe model requires 20 minutes of construction time and 10 minutes of finishing and inspection time. Each
Special model requires 15 minutes of construction time and 15 minutes of finishing and inspection time. The
company has also decided that the Special model must comprise at most 60 percent of the production total.
Formulate this as a linear programming problem.
Answer:
Diff: 2
Topic: FORMULATING LP PROBLEMS
AACSB: Analytic Skills
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86) Determine where the following two constraints intersect.
5X + 23Y ≤ 1000
10X + 26Y ≤ 1600
Answer: (108, 20)
Diff: 1
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
87) Determine where the following two constraints intersect.
2X - 4Y = 800
−X + 6Y ≥ -200
Answer: (500, 50)
Diff: 1
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
88) Two advertising media are being considered for promotion of a product. Radio ads cost $400 each, while
newspaper ads cost $600 each. The total budget is $7,200 per week. The total number of ads should be at least 15,
with at least 2 of each type, and there should be no more than 19 ads in total. The company does not want the
number of newspaper ads to exceed the number of radio ads by more than 25 percent. Each newspaper ad
reaches 6,000 people, 50 percent of whom will respond; while each radio ad reaches 2,000 people, 20 percent of
whom will respond. The company wishes to reach as many respondents as possible while meeting all the
constraints stated. Develop the appropriate LP model for determining the number of ads of each type that should
be placed.
Answer:
Diff: 2
Topic: FORMULATING LP PROBLEMS
AACSB: Analytic Skills
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89) Suppose a linear programming (maximization) problem has been solved and the optimal value of the
objective function is $300. Suppose a constraint is removed from this problem. Explain how this might affect each
of the following:
(a)
the feasible region.
(b)
the optimal value of the objective function.
Answer:
(a)
Removing a constraint may, if the constraint is not redundant, increase the size of the feasible region. It
can never make the feasible region any smaller. If the constraint was active in the solution, removing it will also
result in a new optimal solution. However, removing an essential constraint could cause the problem to become
unbounded.
(b)
Removal of a constraint can only increase or leave the same the size of the feasible region; therefore, the
value of the objective function will either increase or remain the same, assuming the problem has not become
unbounded.
Diff: 2
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM and FOUR SPECIAL CASES IN LP
AACSB: Analytic Skills
90) Consider the following constraints from a two-variable linear program.
(1) X ≥ 0
(2) Y ≥ 0
(3) X + Y ≤ 50
If the optimal corner point lies at the intersection of constraints (2) and (3), what is the optimal solution (X, Y)?
Answer: Y = 0, so X + 0 = 50, or X = 50. Thus the solution is (50, 0).
Diff: 1
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
AACSB: Analytic Skills
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91) Consider a product mix problem, where the decision involves determining the optimal production levels for
products X and Y. A unit of X requires 4 hours of labor in department 1 and 6 hours a labor in department 2. A
unit of Y requires 3 hours of labor in department 1 and 8 hours of labor in department 2. Currently, 1000 hours of
labor time are available in department 1, and 1200 hours of labor time are available in department 2.
Furthermore, 400 additional hours of cross-trained workers are available to assign to either department (or split
between both). Each unit of X sold returns a $50 profit, while each unit of Y sold returns a $60 profit. All units
produced can be sold. Formulate this problem as a linear program. (Hint: Consider introducing other decision
variables in addition to the production amounts for X and Y.)
Answer:
Maximize: 50X + 60Y
Diff: 3
Topic: FORMULATING LP PROBLEMS
AACSB: Analytic Skills
92) A plastic parts supplier produces two types of plastic parts used for electronics. Type 1 requires 30 minutes of
labor and 45 minutes of machine time. Type 2 requires 60 minutes of machine hours and 75 minutes of labor.
There are 600 hours available per week of labor and 800 machine hours available. The demand for custom molds
and plastic parts are identical. Type 1 has a profit margin of $25 a unit and Type 2 have a profit margin of $45 a
unit. The plastic parts supplier must choose the quantity of Product A and Product B to produce which
maximizes profit.
(a)
Formulate this as a linear programming problem.
(b)
Find the solution that gives the maximum profit using either QM for Windows or Excel.
Answer:
(b)
X1 = 914.28, X2 = 114.28
Diff: 2
Topic: FORMULATING LP PROBLEMS and SOLVING FLAIR FURNITURE’S PROBLEM USING QM FOR
WINDOWS and EXCEL
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AACSB: Analytic Skills
93) A company can decide how many additional labor hours to acquire for a given week. Subcontractor workers
will only work a maximum of 20 hours a week. The company must produce at least 200 units of product A, 300
units of product B, and 400 units of product C. In 1 hour of work, worker 1 can produce 15 units of product A, 10
units of product B, and 30 units of product C. Worker 2 can produce 5 units of product A, 20 units of product B,
and 35 units of product C. Worker 3 can produce 20 units of product A, 15 units of product B, and 25 units of
product C. Worker 1 demands a salary of $50/hr, worker 2 demands a salary of $40/hr, and worker 3 demands a
salary of $45/hr. The company must choose how many hours they should contract with each worker to meet their
production requirements and minimize labor cost.
(a)
Formulate this as a linear programming problem.
(b)
Find the optimal solution.
Answer:
(b) X1 = 0, X2 = 9.23, X3 = 7.69
Diff: 3
Topic: FORMULATING LP PROBLEMS and SOLVING FLAIR FURNITURE’S PROBLEM USING QM FOR
WINDOWS and EXCEL
AACSB: Analytic Skills
94) Define dual price.
Answer: The dual price for a constraint is the improvement in the objective function value that results from a
one-unit increase in the right-hand side of the constraint.
Diff: 2
Topic: SENSITIVITY ANALYSIS
95) One basic assumption of linear programming is proportionality. Explain its need.
Answer: Rates of consumption exist and are constant. For example, if the production of 1 unit requires 4 units of
a resource, then if 10 units are produced, 40 units of the resource are required. A change in the variable value
results in a proportional change in the objective function value.
Diff: 2
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
96) One basic assumption of linear programming is divisibility. Explain its need.
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Answer: Solutions can have fractional values and need not be whole numbers. If fractional values would not
make sense, then integer programming would be required.
Diff: 2
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
Quantitative Analysis for Management, 11e (Render)
Chapter 9 Transportation and Assignment Models
1) Transportation and assignment problems are really linear programming techniques called network flow
problems.
Answer: TRUE
Diff: 2
Topic: INTRODUCTION
2) Transportation models may be used when a firm is trying to decide where to locate a new facility.
Answer: TRUE
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
3) A typical transportation problem may ask the question, "How many of X should be shipped to point E from
source A?"
Answer: TRUE
Diff: 1
Topic: THE TRANSPORTATION ALGORITHM
4) The objective of a transportation problem solution is to schedule shipments from sources to destinations while
minimizing total transportation and production costs.
Answer: TRUE
Diff: 1
Topic: THE TRANSPORTATION ALGORITHM
5) In a transportation problem, each destination must be supplied by one and only one source.
Answer: FALSE
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
6) In a transportation problem, a single source may supply something to all destinations.
Answer: TRUE
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
7) In finding the maximum quantity that can be shipped on the least costly route using the stepping-stone
method, one examines the closed path of plus and minus signs drawn and selects the smallest number found in
those squares containing minus signs.
Answer: TRUE
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Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
8) In using the stepping-stone method, the path can turn at any box or cell that is unoccupied.
Answer: FALSE
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
9) Using the stepping-stone method to solve a maximization problem, we would choose the route with the largest
positive improvement index.
Answer: TRUE
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
10) One of the advantages of the stepping-stone method is that if, at a particular iteration, we accidentally choose
a route that is not the best, the only penalty is to perform additional iterations.
Answer: TRUE
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
11) A "balanced problem" exists in a transportation model when the optimal solution has the same amount being
shipped over all paths that have any positive shipment.
Answer: FALSE
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
12) It is possible to find an optimal solution to a transportation problem that is degenerate.
Answer: TRUE
Diff: 2
Topic: SPECIAL SITUATIONS WITH THE TRANSPORTATION ALGORITHM
13) A solution to the transportation problem can become degenerate at any iteration.
Answer: TRUE
Diff: 2
Topic: SPECIAL SITUATIONS WITH THE TRANSPORTATION ALGORITHM
14) The transportation algorithm can be used to solve both minimization problems and maximization problems.
Answer: TRUE
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
15) Assignment problems involve determining the most efficient assignment of people to projects, salesmen to
territories, contracts to bidders, and so on.
Answer: TRUE
Diff: 1
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Topic: THE ASSIGNMENT ALGORITHM
16) The objective of an assignment problem solution most often is to minimize the total costs or time of
performing the assigned tasks.
Answer: TRUE
Diff: 2
Topic: THE ASSIGNMENT ALGORITHM
17) In the assignment problem, the costs for a dummy row will be equal to the lowest cost of the column for each
respective cell in that row.
Answer: FALSE
Diff: 2
Topic: THE ASSIGNMENT ALGORITHM
18) The Hungarian method is designed to solve transportation problems efficiently.
Answer: FALSE
Diff: 2
Topic: THE ASSIGNMENT ALGORITHM
19) Maximization assignment problems can easily be converted to minimization problems by subtracting each
rating from the largest rating in the table.
Answer: TRUE
Diff: 2
Topic: THE ASSIGNMENT ALGORITHM
20) In a transportation problem, a dummy source is given a zero cost, while in an assignment problem, a dummy
source is given a very high cost.
Answer: FALSE
Diff: 2
Topic: SPECIAL SITUATIONS WITH THE TRANSPORTATION ALGORITHM
Table 9-1
21) What is the total cost represented by the solution shown in Table 9-1?
A) 60
B) 2500
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C) 2600
D) 500
E) None of the above
Answer: D
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
AACSB: Analytic Skills
22) What is the value of the improvement index for cell B1 shown in Table 9-1?
A) -50
B) +3
C) +2
D) +1
E) None of the above
Answer: C
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
AACSB: Analytic Skills
Table 9-2
23) In Table 9-2, cell A3 should be selected to be filled in the next solution. If this was selected as the cell to be
filled, and the next solution was found using the appropriate stepping-stone path, how many units would be
assigned to this cell?
A) 10
B) 15
C) 20
D) 30
E) None of the above
Answer: B
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
AACSB: Analytic Skills
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Table 9-3
The following improvements are proved for Table 9-3:
Cell
A1
A3
B2
B-Dummy
C1
C2
Improvement Index
+2
+6
+1
+2
+2
+1
24) The cell improvement indices for Table 9-3 suggest that the optimal solution has been found. Based on this
solution, how many units would actually be sent from source C?
A) 10
B) 170
C) 180
D) 250
E) None of the above
Answer: B
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
AACSB: Analytic Skills
25) In Table 9-3, suppose shipping cost from source C to point 2 was 8, which below would be true?
A) There would be multiple optimal solutions.
B) The minimum possible total cost would decrease.
C) The minimum possible total cost would increase.
D) Another dummy column would be needed.
E) None of the above
Answer: A
Diff: 2
Topic: SPECIAL SITUATIONS WITH THE TRANSPORTATION ALGORITHM
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AACSB: Analytic Skills
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26) Both transportation and assignment problems are members of a category of LP techniques called ________.
A) transshipment problems
B) Hungarian problems
C) source-destination problems
D) supply and demand problems
E) network flow problems
Answer: E
Diff: 2
Topic: INTRODUCTION
27) Transportation models can be used for which of the following decisions?
A) facility location
B) production mix
C) media selection
D) portfolio selection
E) employee shift scheduling
Answer: A
Diff: 1
Topic: THE TRANSPORTATION ALGORITHM
28) When using a general LP model for transportation problems, if there are 4 sources and 3 destinations, which
of the following statements is true?
A) There are typically 4 decision variables and 3 constraints.
B) There are typically 12 decision variables and 7 constraints.
C) There are typically 7 decision variables and 7 constraints.
D) There are typically 12 decision variables and 12 constraints.
E) There are typically 12 decision variables and 3 constraints.
Answer: B
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
29) The two most common objectives for the assignment problem are the minimization of ________.
A) uncertainty or inexperience
B) total costs or inexperience
C) total costs or total time
D) total time or inexperience
E) total costs or uncertainty
Answer: C
Diff: 2
Topic: THE ASSIGNMENT ALGORITHM
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30) Assuming that Table 9-4 represents the results of an iteration of a transportation model,
Table 9-4
The next tableau will be:
A)
B)
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C)
D)
E) None of the above
Answer: B
Diff: 3
Topic: THE TRANSPORTATION ALGORITHM
AACSB: Analytic Skills
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Table 9-5
31) Table 9-5 represents a solution that is
A) clearly optimal for a minimization objective.
B) degenerate.
C) infeasible.
D) All of the above
E) None of the above
Answer: B
Diff: 2
Topic: SPECIAL SITUATIONS WITH THE TRANSPORTATION ALGORITHM
AACSB: Analytic Skills
Table 9-6
32) In Table 9-6, if cell A3 is filled on the next iteration, what is the improvement in the objective function?
A) 60
B) 30
C) 530
D) 590
E) None of the above
Answer: B
Diff: 2
Topic: SPECIAL SITUATIONS WITH THE TRANSPORTATION ALGORITHM
AACSB: Analytic Skills
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33) A transportation problem
A) is a special case of the linear programming problem.
B) can be solved by linear programming, but is solved more efficiently by a special-purpose algorithm.
C) may give an initial feasible solution rather than the optimal solution.
D) requires the same assumptions that are required for linear programming problems.
E) All of the above
Answer: E
Diff: 2
Topic: VARIOUS
Table 9-7
34) Table 9-7 illustrates a(n)
A) optimal solution.
B) degenerate solution.
C) unbounded solution.
D) infeasible solution.
E) None of the above
Answer: D
Diff: 2
Topic: SPECIAL SITUATIONS WITH THE TRANSPORTATION ALGORITHM
AACSB: Analytic Skills
35) The only restriction we place on the initial solution of a transportation problem is that
A) we must have nonzero quantities in a majority of the boxes.
B) all constraints must be satisfied.
C) demand must be less than supply.
D) we must have a number (equal to the number of rows plus the number of columns minus one) of boxes that
contain nonzero quantities.
E) None of the above
Answer: B
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
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36) Which of the following is used to summarize conveniently and concisely all relevant data and to keep track of
algorithm computations?
A) source-destination matrix
B) Hungarian table
C) stepping-stone grid
D) transportation table
E) tabulation report
Answer: D
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
37) In Table 9-8, which cell should be filled on the next iteration?
Table 9-8
A) A1
B) ADummy
C) B2
D) C1
E) C2
Answer: B
Diff: 3
Topic: THE TRANSPORTATION ALGORITHM
AACSB: Analytic Skills
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Table 9-9
38) The solution presented in Table 9-9 is
A) infeasible.
B) degenerate.
C) unbounded.
D) optimal.
E) None of the above
Answer: D
Diff: 3
Topic: THE TRANSPORTATION ALGORITHM
AACSB: Analytic Skills
Table 9-10
39) What is wrong with Table 9-10?
A) The solution is infeasible.
B) The solution is degenerate.
C) The solution is unbounded.
D) Nothing is wrong.
E) There are too many filled cells.
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Answer: E
Diff: 2
Topic: SPECIAL SITUATIONS WITH THE TRANSPORTATION ALGORITHM
AACSB: Analytic Skills
40) Which of the following statements concerning the transshipment problem are false?
A) The number of units shipped into a transshipment point should be equal to the number of units shipped out.
B) There can be constraints on the number of units shipped out of an origin point.
C) There can be constraints on the number of units shipped into a destination point.
D) The transshipment problem can be solved with linear programming.
E) Any units shipped from one origin point must all go to the same destination point.
Answer: E
Diff: 2
Topic: THE TRANSSHIPMENT PROBLEM
41) What is said to exist when total demand equals total supply in a transportation problem?
A) an equalized problem
B) an equilibrialized problem
C) a harmonized problem
D) a balanced problem
E) This situation can never occur.
Answer: D
Diff: 1
Topic: THE TRANSPORTATION ALGORITHM
Table 9-11
42) A company must assign mechanics to each of four jobs. The time involved varies according to individual
abilities. Table 9-11 shows how many minutes it takes each mechanic to perform each job. If the optimal
assignments are made, how many total minutes would be required for completing the jobs?
A) 0
B) 4
C) 17
D) 16
E) None of the above
Answer: D
Diff: 3
Topic: THE ASSIGNMENT ALGORITHM
AACSB: Analytic Skills
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Table 9-12
43) Given Table 9-12, the final table for an assignment problem, who should be assigned to job 2?
A) worker A
B) worker C
C) either worker A or worker C
D) neither worker A nor worker C
E) worker D
Answer: B
Diff: 2
Topic: THE ASSIGNMENT ALGORITHM
AACSB: Analytic Skills
Table 9-13
44) Table 9-13 provides information about a transportation problem. This problem is
A) unbounded.
B) unbalanced.
C) infeasible.
D) All of the above
E) None of the above
Answer: B
Diff: 2
Topic: SPECIAL SITUATIONS WITH THE TRANSPORTATION ALGORITHM
AACSB: Analytic Skills
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45) Which of the following statements concerning transportation and assignment models is false?
A) The transportation, transshipment, and assignment problems can all be solved using linear programming.
B) A common objective is cost minimization.
C) Both transportation and assignment models involve the distribution of goods from sources to destinations.
D) The assignment problem can have a maximization objective.
E) The transshipment problem is a special class of transportation problems.
Answer: C
Diff: 2
Topic: VARIOUS
46) Which of the following is not part of the transportation algorithm?
A) northwest corner rule
B) stepping-stone method
C) balanced transportation table
D) portfolio selection
E) Hungarian method
Answer: D
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
47) Which technique requires that we start in the upper-left-hand cell of the table and allocate units to shipping
routes in a "stair step" fashion?
A) upper-left rule
B) stair step method
C) northwest corner rule
D) Vogel's approximation method
E) MODI
Answer: C
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
48) If items being transported must go through an intermediate point before reaching a final destination, then this
situation is known as a(n) ________.
A) transshipment problem
B) assignment problem
C) transportation problem
D) intermediate point problem
E) None of the above
Answer: A
Diff: 2
Topic: THE TRANSSHIPMENT PROBLEM
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49) Which of the following accurately describes steps of the northwest corner rule, after making the initial
allocation of units in the northwest cell?
A) Move down first, and then move right.
B) Move right first, and then move down.
C) Move right or down first, depending on whether the demand requirement or the supply capacity, respectively,
is exhausted first.
D) Move right or down first, depending on whether the supply capacity or the demand requirement, respectively,
is exhausted first.
E) Move diagonally first.
Answer: C
Diff: 3
Topic: THE TRANSPORTATION ALGORITHM
50) When using the stepping-stone method, what is the maximum amount that can be shipped on the new route?
A) the smallest number found in the squares with minus signs
B) the smallest number found in the squares with plus signs
C) the smallest number along the closed path
D) the minimum of the demand requirement for that column and the supply capacity for that row
E) the largest number found on the squares with minus signs
Answer: A
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
Table 9-14
51) The solution presented in Table 9-14 is
A) infeasible.
B) degenerate.
C) unbounded.
D) optimal.
E) Both B and D
Answer: E
Diff: 3
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Topic: VARIOUS
AACSB: Analytic Skills
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Table 9-15
52) The solution shown in Table 9-15 is
A) infeasible.
B) degenerate.
C) unbounded.
D) optimal.
E) None of the above
Answer: E
Diff: 3
Topic: VARIOUS
AACSB: Analytic Skills
53) In a transshipment problem involving 3 origins, 2 intermediate points, and 4 final destinations, what is the
maximum number of decision variables?
A) 24
B) 9
C) 14
D) 7
E) 20
Answer: A
Diff: 2
Topic: THE TRANSSHIPMENT PROBLEM
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Table 9-16
54) The solution shown in Table 9-16 is
A) infeasible.
B) one of a number of alternate solutions.
C) unbounded.
D) optimal.
E) None of the above
Answer: D
Diff: 3
Topic: THE TRANSPORTATION ALGORITHM
AACSB: Analytic Skills
55) A certain firm has four different operations that must be assigned to four locations. The profit (in thousands
of dollars) associated with each operation at each location is presented below. The firm's vice president would
like to assign the various operations so that the total profit is maximized. Find the appropriate assignments.
Answer: Assign W to 2, X to 4, Y to 3, and Z to 1. Total profit = $48 (thousand)
Diff: 3
Topic: THE ASSIGNMENT ALGORITHM
AACSB: Analytic Skills
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56) What is the overall objective in applying the transportation method to the facility location problem?
A) minimize the distance traveled
B) minimize the number of items shipped
C) maximize the value of items shipped
D) minimize the cost of the distribution system
E) None of the above
Answer: D
Diff: 2
Topic: FACILITY LOCATION ANALYSIS
57) An artificial source added to a transportation table when total demand is greater than total supply is called
________.
A) excess source
B) filler source
C) dummy source
D) demand source
E) supply source
Answer: C
Diff: 1
Topic: SPECIAL SITUATIONS WITH THE TRANSPORTATION ALGORITHM
58) Which of the following techniques can be used for moving from an initial feasible solution to an optimal
solution in a transportation problem?
A) Hungarian method
B) stepping-stone method
C) northwest corner rule
D) Vogel's approximation method
E) All of the above
Answer: B
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
59) Which of the following is an applicable characteristic in using the stepping-stone method?
A) Only an unoccupied square may be used as a "stepping-stone."
B) Only an occupied square may be used as a "stepping-stone."
C) Only the column and row with the highest factory capacity may be used as a "stepping-stone."
D) All of the above
E) None of the above
Answer: B
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
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60) After testing each unused cell by the stepping-stone method in the transportation problem and finding only
one cell with a negative improvement index,
A) once you make that improvement, you would definitely have an optimal solution.
B) you would make that improvement and then check all unused cells again.
C) you could stop because you already had the optimal solution.
D) you should check to be sure that you don't have to add a dummy source or dummy destination.
E) None of the above
Answer: B
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
61) In the transportation problem, using the stepping-stone method,
A) you may not skip over an empty cell.
B) you may not skip over a used cell.
C) your path may not cross over itself.
D) if you have an optimal solution and get an improvement index of zero, there is another optimal solution.
E) None of the above
Answer: D
Diff: 2
Topic: SPECIAL SITUATIONS WITH THE TRANSPORTATION ALGORITHM
62) If we want to quickly arrive at a "feasible," but not necessarily "optimal" solution to the transportation
problem, we will use the
A) stepping-stone method.
B) northwest corner rule.
C) Vogel's approximation method.
D) MODI method.
E) Any of the above
Answer: B
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
63) If the total supply from the sources does not equal the total demand from the destinations in the
transportation problem,
A) and if supply is greater than demand, add a dummy source or factory.
B) the amount put in a dummy source or destination should make supply and demand equal.
C) and if demand is greater than supply, add a dummy destination or warehouse.
D) All of the above
E) None of the above
Answer: B
Diff: 2
Topic: SPECIAL SITUATIONS WITH THE TRANSPORTATION ALGORITHM
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64) In a transportation problem, degeneracy occurs when
A) the number of used (or full) cells does not equal the number of rows plus columns minus one.
B) in an initial solution, both a row total and a column total are satisfied simultaneously.
C) during an improvement, two negative cells contain the same smallest amount.
D) All of the above
E) None of the above
Answer: D
Diff: 2
Topic: SPECIAL SITUATIONS WITH THE TRANSPORTATION ALGORITHM
65) Practically speaking, multiple optimal solutions ________.
A) are infeasible
B) are unbounded
C) are degenerate
D) are unbalanced
E) provide management with greater flexibility in selecting and using resources
Answer: E
Diff: 1
Topic: SPECIAL SITUATIONS WITH THE TRANSPORTATION ALGORITHM
66) Which of the following is not considered a special situation with the transportation algorithm?
A) unbalanced transportation problems
B) degeneracy
C) unconstrained transportation problems
D) more than one optimal solution
E) maximization transportation problems
Answer: C
Diff: 2
Topic: SPECIAL SITUATIONS WITH THE TRANSPORTATION ALGORITHM
67) Which of the following is not a step in the Hungarian method of assignment?
A) find the opportunity-cost table
B) test for an optimal assignment
C) enumerate all possible solutions
D) revise the opportunity-cost table
E) None of the above
Answer: C
Diff: 2
Topic: THE ASSIGNMENT ALGORITHM
68) Why don't we want to use the transportation algorithm to solve the assignment problem?
A) It would likely lead to an unbounded solution.
B) It would likely lead to a degenerate solution.
C) It would likely lead to an infeasible solution.
D) It would likely lead to multiple optima.
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E) It would likely lead to an unbalanced solution.
Answer: B
Diff: 2
Topic: THE ASSIGNMENT ALGORITHM
69) In an assignment problem
A) the number of rows and columns must be equal.
B) the number of rows must exceed the number of columns.
C) the number of rows must equal or exceed the number of columns.
D) the number of columns must equal or exceed the number of rows.
E) None of the above
Answer: A
Diff: 2
Topic: THE ASSIGNMENT ALGORITHM
70) In revising the opportunity cost table of the assignment problem, after drawing lines through all of the zeros,
A) the smallest uncovered number is added to all zeros.
B) the smallest uncovered number is added to all uncovered numbers.
C) the largest uncovered number is added to all uncovered numbers.
D) the smallest uncovered number is added to all numbers at the intersection of lines.
E) the largest uncovered number is added to all numbers at the intersection of lines.
Answer: D
Diff: 2
Topic: THE ASSIGNMENT ALGORITHM
71) Which of the following methods is used only with the assignment problem?
A) the Hungarian method
B) stepping-stone method
C) MODI method
D) Vogel's approximation method
E) the simplex method
Answer: A
Diff: 1
Topic: THE ASSIGNMENT ALGORITHM
72) Objectives of the assignment problem can include
A) minimize total costs.
B) minimize total time to perform the tasks at hand.
C) minimize opportunity costs.
D) maximize profit.
E) All of the above
Answer: E
Diff: 2
Topic: THE ASSIGNMENT ALGORITHM
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73) In solving maximization assignment problems,
A) just reverse all the decision rules used in the minimizing algorithm (if it says subtract, now add, and so on).
B) convert the problem to an equivalent minimization problem.
C) use the Australian transformation process and convert the data.
D) All of the above
E) None of the above
Answer: B
Diff: 2
Topic: THE ASSIGNMENT ALGORITHM
74) Which tableau is the solution to the transportation problem depicted below?
Table 9-17
A)
B)
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C)
D)
E) None of the above
Answer: A
Diff: 3
Topic: VARIOUS
AACSB: Analytic Skills
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75) Which tableau is the solution to the following transportation table?
Table 9-18
A)
B)
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C)
D)
E) None of the above
Answer: E
Diff: 3
Topic: VARIOUS
AACSB: Analytic Skills
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76) Table 9-19 describes a transportation problem:
Table 9-19
(a) Use the northwest corner method to get an initial solution.
(b) What is the cost of the initial solution?
(c) Use the stepping-stone method to find the optimal solution.
(d) What is the cost of the optimal solution?
(e) Is there an alternate optimal solution?
Answer:
(a)
(b)
Cost = 280
(c)
Optimal solution:
(d)
(e)
Cost = 210
no
Diff: 3
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Topic: VARIOUS
AACSB: Analytic Skills
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77) Four projects must be completed, and each of four employees will be assigned to work on exactly one of the
four projects. The table below presents an estimate of the cost that each employee would incur if working on the
respective projects. What is the minimum-cost assignment of workers to projects?
Answer: MaryProject 2, ElizabethProject 4, StevenProject 1, JoshuaProject 3
Diff: 2
Topic: THE ASSIGNMENT ALGORITHM
AACSB: Analytic Skills
78) SE Appliances manufacturers refrigerators in Richmond, Charlotte, and Atlanta. Refrigerators then must be
shipped to meet demand in Washington, New York, and Miami. The table below lists the shipping costs, supply,
and demand information.
How many units should be shipped from each plant to each retail store in order to minimize shipping costs?
Answer: Ship 1000 units from Richmond to New York, 1000 units from Charlotte to Washington, 800 units from
Atlanta to New York, and 1200 units from Atlanta to Miami, with the 500 from Charlotte to the Dummy
unshipped.
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
AACSB: Analytic Skills
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79) Neki Sports Company manufacturers treadmills in factories located in Pittsburgh and Kansas City. These are
shipped to regional distribution centers in Chicago, Phoenix, and Philadelphia. Ultimately they are delivered to
supply houses in New York and Los Angeles. The available supplies at the factories, demands at the final
destinations, and shipping costs are illustrated in the table below.
Formulate this problem as a linear program.
Answer: Let (1) = Pittsburgh, (2) = Kansas City, (3) = Chicago, (4) = Phoenix, (5) = Philadelphia, (6) = New York,
and (7) = Los Angeles
Let xij = the number of units shipped from location i to location j.
The LP is as follows:
Minimize total cost = 4x13 + 3x23 + 8x14+ 6x24 + 2x15+ 5x25 + 5x36 + 8x46 + 2x56 + 7x37 + 3x47 + 9x57
Subject to:
x13 + x14 + x15 ≤ 1500
x23 + x24 + x25 ≤ 1000
x13 + x23 = x36 + x37
x14 + x24 = x46 + x47
x15 + x25 = x56 + x57
x36 + x46 + x56 = 1200
x37 + x47 + x57 = 800
All xij ≥ 0
Diff: 2
Topic: THE TRANSSHIPMENT PROBLEM
AACSB: Analytic Skills
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80) Neki Sports Company manufacturers treadmills in factories located in Pittsburgh and Kansas City. These are
shipped to regional distribution centers in Chicago, Phoenix, and Philadelphia. Ultimately they are delivered to
supply houses in New York and Los Angeles. The available supplies at the factories, demands at the final
destinations, and shipping costs are illustrated in the table below.
Determine how many units should be shipped for all possible origin and destination points (final or intermediate)
in the distribution network in order to minimize shipping costs.
Answer: The best solution is to ship 1200 units from Pittsburgh to Philadelphia, ship 800 units from Kansas City
to Phoenix, then 1200 units from Philadelphia to New York, and 800 units from Phoenix to Los Angeles.
Diff: 2
Topic: THE TRANSSHIPMENT PROBLEM
AACSB: Analytic Skills
81) Describe a general transportation problem.
Answer: a specific case of linear programming concerned with scheduling shipments from sources to
destinations while minimizing transportation costs
Diff: 2
Topic: INTRODUCTION
82) What is meant by a balanced transportation problem?
Answer: a situation in which total demand equals total supply exactly
Diff: 2
Topic: THE TRANSPORTATION ALGORITHM
83) The assignment problem is a special case of the transportation problem. So, then, why is it not recommended
to use the transportation algorithm to solve the assignment problem?
Answer: It would result in a severe degeneracy problem.
Diff: 2
Topic: THE ASSIGNMENT ALGORITHM
84) When is a dummy destination added to a transportation problem?
Answer: when total supply exceeds total demand
Diff: 2
Topic: SPECIAL SITUATIONS WITH THE TRANSPORTATION ALGORITHM
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Quantitative Analysis for Management, 11e (Render)
Chapter 11 Network Models
1) The minimal-spanning tree technique finds the shortest route to a series of destinations.
Answer: FALSE
Diff: 2
Topic: INTRODUCTION
2) In the minimal-spanning tree technique, it is necessary to start at the last node in the network.
Answer: FALSE
Diff: 2
Topic: MINIMAL-SPANNING TREE PROBLEM
3) The maximal-flow technique would be helpful to city planners in determining how freeways should be
expanded.
Answer: TRUE
Diff: 2
Topic: MAXIMAL-FLOW PROBLEM
4) The minimal-spanning tree technique determines the path through the network that connects all the points
while minimizing total distance.
Answer: TRUE
Diff: 2
Topic: INTRODUCTION
5) The shortest-route technique is the same as the minimal-spanning tree technique.
Answer: FALSE
Diff: 1
Topic: INTRODUCTION
6) Busy highways are often analyzed with the maximal-flow technique.
Answer: TRUE
Diff: 2
Topic: MAXIMAL-FLOW PROBLEM
7) Transportation companies would definitely be interested in the shortest-route technique to optimize travel.
Answer: TRUE
Diff: 2
Topic: SHORTEST-ROUTE PROBLEM
8) Cable television companies would employ the shortest-route technique to lay out the cables connecting
individual houses.
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Answer: FALSE
Diff: 2
Topic: MINIMAL-SPANNING TREE PROBLEM
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9) We may begin the maximal-flow technique by picking an arbitrary path through the network.
Answer: TRUE
Diff: 2
Topic: MAXIMAL-FLOW PROBLEM
10) The maximal-flow technique finds the maximum flow of any quantity or substance through a network.
Answer: TRUE
Diff: 1
Topic: INTRODUCTION
11) The maximal-flow technique might be used by the U.S. Army Corps of Engineers to study water run-off in an
attempt to minimize the danger from floods.
Answer: TRUE
Diff: 2
Topic: MAXIMAL-FLOW PROBLEM
12) The shortest-route technique might be used by someone planning a vacation in order to minimize the
required amount of driving.
Answer: TRUE
Diff: 2
Topic: SHORTEST-ROUTE PROBLEM
13) The points on the network are referred to as nodes.
Answer: TRUE
Diff: 2
Topic: INTRODUCTION
14) Lines connecting nodes on a network are called links.
Answer: FALSE
Diff: 2
Topic: INTRODUCTION
15) A traveling salesperson might use the shortest route technique to minimize the distance traveled to reach one
of his/her customers.
Answer: TRUE
Diff: 2
Topic: SHORTEST-ROUTE PROBLEM
16) In the minimal-spanning tree technique, if there is a tie for the nearest node, that suggests that there may be
more than one optimal solution.
Answer: TRUE
Diff: 2
Topic: MINIMAL-SPANNING TREE PROBLEM
17) The maximal-flow model might be of use to an engineer looking for spare capacity in an oil pipeline system.
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Answer: TRUE
Diff: 2
Topic: MAXIMAL-FLOW PROBLEM
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18) The shortest-route model assumes that one is trying to connect two end points in the shortest manner
possible, rather than attempting to connect all the nodes in the model.
Answer: TRUE
Diff: 2
Topic: SHORTEST-ROUTE PROBLEM
19) In the maximal-flow technique, a zero (0) means no flow or a one-way arc.
Answer: TRUE
Diff: 2
Topic: MAXIMAL-FLOW PROBLEM
20) The maximal-flow model assumes that there is a net flow from "source" to "sink."
Answer: TRUE
Diff: 2
Topic: MAXIMAL-FLOW PROBLEM
21) If your goal was to construct a network in which all points were connected and the distance between them
was as short as possible, the technique that you would use is
A) shortest-route.
B) maximal-flow.
C) shortest-spanning tree.
D) minimal-flow.
E) minimal-spanning tree.
Answer: E
Diff: 2
Topic: INTRODUCTION
22) The minimal-spanning technique would best be used
A) to assign workers to jobs in the cheapest manner.
B) to determine LAN network wiring within a building.
C) to minimize traffic flow on a busy highway.
D) by a trucking company making frequent but repeatable drops.
E) to determine the number of units to ship from each source to each destination.
Answer: B
Diff: 2
Topic: MINIMAL-SPANNING TREE PROBLEM
23) The maximal-flow technique would best be used
A) to assign workers to jobs in the cheapest manner.
B) to determine the number of units to ship from each source to each destination.
C) to determine LAN network wiring within a building.
D) to maximize traffic flow on a busy highway.
E) by a trucking company making frequent but repeatable drops.
Answer: D
Diff: 2
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Topic: MAXIMAL-FLOW PROBLEM
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24) A line in a network that may represent a path or a route is called a(n) ________.
A) arc
B) branch
C) line
D) fork
E) sink
Answer: A
Diff: 1
Topic: INTRODUCTION
25) A point in the network, that is at the beginning or end of a route is called a(n) ________.
A) arc
B) branch
C) line
D) node
E) source
Answer: D
Diff: 1
Topic: INTRODUCTION
26) The final node or destination in a network is called a(n) ________.
A) arc
B) branch
C) source
D) mouth
E) sink
Answer: E
Diff: 1
Topic: MAXIMAL-FLOW PROBLEM
27) The origin or beginning node in a network is called ________.
A) home
B) delta
C) source
D) mouth
E) sink
Answer: C
Diff: 1
Topic: MAXIMAL-FLOW PROBLEM
28) A technique that allows a researcher to determine the greatest amount of material that can move through a
network is called
A) maximal-flow.
B) maximal-spanning.
C) shortest-route.
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D) maximal-tree.
Answer: B
Diff: 2
Topic: INTRODUCTION
29) The first step in the maximal-flow technique is to
A) pick the node with the maximum flow.
B) pick any path with some flow.
C) eliminate any node that has a zero flow.
D) add a dummy flow from the start to the finish.
E) None of the above
Answer: B
Diff: 2
Topic: MAXIMAL-FLOW PROBLEM
30) The shortest-route technique would best be used to ________
A) assign workers to jobs in the cheapest manner.
B) determine the number of units to ship from each source to each destination.
C) determine the amount of LAN network wiring within a building.
D) minimize the amount of traffic flow on a busy highway.
E) determine the path for a truck making frequent but repeatable drops.
Answer: E
Diff: 2
Topic: SHORTEST-ROUTE PROBLEM
31) When using the shortest-route technique, the first step is to
A) connect the nearest node that minimizes the total distance to the origin.
B) trace the path from the warehouse to the plant.
C) determine the average distance traveled from source to end.
D) find the nearest node to the origin and put a distance box by the node.
E) None of the above
Answer: D
Diff: 2
Topic: SHORTEST-ROUTE PROBLEM
32) The shortest-route technique might be logically used for
A) finding the longest time to travel between two points.
B) finding the shortest travel distance between two points.
C) finding the most scenic route to allow travel to several places during a trip on spring break.
D) connecting all the points of a network together while minimizing the distance between them.
E) None of the above
Answer: B
Diff: 2
Topic: INTRODUCTION
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33) All the nodes must be connected in which of the following techniques?
A) minimal-flow
B) maximal-spanning tree
C) shortest-route
D) maximal-flow
E) minimal-spanning tree
Answer: E
Diff: 1
Topic: MINIMAL-SPANNING TREE PROBLEM
34) The minimal-spanning tree technique would best be used
A) by a forest ranger seeking to minimize the risk of forest fires.
B) by a telephone company attempting to lay out wires in a new housing development.
C) by an airline laying out flight routes.
D) None of the above
E) All of the above
Answer: B
Diff: 2
Topic: MINIMAL-SPANNING TREE PROBLEM
35) Which of the following techniques is not discussed in Chapter 11?
A) shortest-route
B) maximal-flow
C) linear programming
D) minimal-flow
E) minimal-spanning tree
Answer: D
Diff: 1
Topic: VARIOUS
36) The maximal-flow technique might be used
A) to help design the moving sidewalks transporting passengers from one terminal to another in a busy airport.
B) by someone designing the traffic approaches to an airport.
C) by someone attempting to design roads that would limit the flow of traffic through an area.
D) All of the above
E) None of the above
Answer: D
Diff: 2
Topic: MAXIMAL-FLOW PROBLEM
37) Which of the following problems can be solved using linear programming?
A) maximal-flow problem
B) shortest-route problem
C) minimal-spanning tree problem
D) A and B
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E) A, B, and C
Answer: D
Diff: 2
Topic: VARIOUS
38) Which of the following problems can be solved as a linear program using binary decision variables?
A) maximal-flow problem
B) shortest-route problem
C) minimal-spanning tree problem
D) A and B
E) A, B, and C
Answer: B
Diff: 2
Topic: SHORTEST-ROUTE PROBLEM
39) Which of the following problems can be solved as a linear program using integer decision variables?
A) maximal-flow problem
B) shortest-route problem
C) minimal-spanning tree problem
D) A and B
E) A, B, and C
Answer: A
Diff: 2
Topic: MAXIMAL-FLOW PROBLEM
40) The second step in the maximal-flow technique is to
A) pick the node with the maximum flow.
B) pick any path with some flow.
C) decrease the flow as much as possible.
D) add capacity to the path with minimum flow.
E) find the arc on the previously chosen path with the smallest flow capacity available.
Answer: E
Diff: 2
Topic: MAXIMAL-FLOW PROBLEM
41) The shortest-route technique would best be used to
A) plan the routes for a vacation driving tour.
B) plan the route for a school bus.
C) determine the path for a truck making frequent runs from a factory to a warehouse.
D) All of the above
E) None of the above
Answer: D
Diff: 2
Topic: SHORTEST-ROUTE PROBLEM
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42) When using the shortest-route technique, the second step is to
A) find the next-nearest node to the origin and put the distance in a box by the node.
B) trace the path from the warehouse to the plant.
C) determine the average distance traveled from source to end.
D) find the nearest node to the origin and put a distance box by the node.
E) None of the above
Answer: A
Diff: 2
Topic: SHORTEST-ROUTE PROBLEM
43) In network models, the lines connecting the nodes are called ________.
A) bridges
B) arrows
C) spans
D) arcs
E) links
Answer: D
Diff: 2
Topic: INTRODUCTION
44) Given the following distances between destination nodes, what is the minimum distance that connects all the
nodes?
From
1
2
1
To
2
3
3
Distance
300
150
200
A) 450
B) 150
C) 350
D) 650
E) None of the above
Answer: C
Diff: 2
Topic: MINIMAL-SPANNING TREE PROBLEM
AACSB: Analytic Skills
45) Given the following distances between destination nodes, what is the minimum distance that connects all the
nodes?
From
1
1
2
To
2
3
3
Distance
200
300
350
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2
3
4
4
350
250
A) 100
B) 750
C) 850
D) 900
E) None of the above
Answer: B
Diff: 2
Topic: MINIMAL-SPANNING TREE PROBLEM
AACSB: Analytic Skills
129
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46) Given the following distances between destination nodes, what is the minimum distance that connects all the
nodes?
From
1
2
1
2
3
4
3
To
2
4
3
3
4
5
5
Distance
100
150
200
50
175
250
300
A) 100
B) 150
C) 550
D) 1225
E) None of the above
Answer: C
Diff: 2
Topic: MINIMAL-SPANNING TREE PROBLEM
AACSB: Analytic Skills
47) Given the following distances between destination nodes, what is the minimum distance that connects all the
nodes?
From
1
1
2
2
1
3
3
4
To
2
3
3
5
4
4
5
5
Distance
100
50
200
325
50
350
400
450
A) 300
B) 525
C) 675
D) 1925
E) None of the above
Answer: B
Diff: 2
Topic: MINIMAL-SPANNING TREE PROBLEM
AACSB: Analytic Skills
130
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48) Pipeline fluid flows are indicated below. Determine the maximum flow from Node 1 to Node 3.
From
Node
1
3
1
2
2
3
To
Node
3
1
2
1
3
2
Fluid
Flow
400
100
300
0
100
100
A) 100
B) 400
C) 500
D) 700
E) None of the above
Answer: C
Diff: 2
Topic: MAXIMAL-FLOW PROBLEM
AACSB: Analytic Skills
49) Pipeline fluid flows are indicated below. Determine the maximum flow from Node 1 to Node 4.
From
Node
1
2
1
4
1
3
2
4
3
4
To
Node
2
1
4
1
3
1
4
2
4
3
Fluid
Flow
400
0
200
200
200
0
200
200
300
300
A) 200
B) 300
C) 600
D) 700
E) None of the above
Answer: C
Diff: 2
Topic: MAXIMAL-FLOW PROBLEM
131
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AACSB: Analytic Skills
132
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50) Find the shortest route from Node 1 to Node 4 using the shortest-route technique.
From
Node
1
1
2
2
3
To
Node
2
3
3
4
4
Distance
300
200
50
250
450
A) 650
B) 450
C) 550
D) 500
E) 800
Answer: D
Diff: 2
Topic: SHORTEST-ROUTE PROBLEM
AACSB: Analytic Skills
51) Find the shortest route from Node 1 to Node 4.
From
Node
1
1
1
2
2
3
To
Node
2
3
4
3
4
4
Distance
250
400
600
50
300
200
A) 750
B) 500
C) 550
D) 600
E) 50
Answer: B
Diff: 2
Topic: SHORTEST-ROUTE PROBLEM
AACSB: Analytic Skills
133
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52) Find the shortest route from Node 1 to Node 6.
From
Node
1
1
2
2
4
3
3
5
To
Node
2
3
4
3
6
4
5
6
Distance
150
200
200
50
100
300
350
100
A) 300
B) 450
C) 550
D) 650
E) None of the above
Answer: B
Diff: 2
Topic: SHORTEST-ROUTE PROBLEM
AACSB: Analytic Skills
53) Given the following distances between destination nodes, what is the minimum distance that connects all the
nodes?
From
1
2
1
2
3
4
To
2
3
3
4
5
5
Distance
120
100
200
150
90
170
A) 290
B) 310
C) 620
D) 460
E) None of the above
Answer: D
Diff: 2
Topic: MINIMAL-SPANNING TREE PROBLEM
AACSB: Analytic Skills
134
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54) Given the following distances between destination nodes, what is the minimum distance that connects all the
nodes?
From
1
1
1
2
2
3
3
4
4
5
To
2
3
5
3
4
4
5
5
6
6
Distance
200
300
400
300
400
200
200
100
300
400
A) 1000
B) 800
C) 700
D) 1100
E) None of the above
Answer: D
Diff: 3
Topic: MINIMAL-SPANNING TREE PROBLEM
AACSB: Analytic Skills
55) Given the following distances between destination nodes, what is the minimum distance that connects all the
nodes?
From
1
1
2
2
2
3
3
4
4
5
To
2
3
3
4
5
4
5
5
6
6
Distance
100
200
100
150
200
150
300
250
200
100
A) 900
B) 650
C) 400
D) 1200
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E) None of the above
Answer: B
Diff: 3
Topic: MINIMAL-SPANNING TREE PROBLEM
AACSB: Analytic Skills
56) Given the following distances between destination nodes, what is the minimum distance that connects all the
nodes?
From
1
1
2
2
1
3
3
3
4
4
5
To
2
3
3
5
4
4
5
6
5
6
6
Distance
100
50
200
300
50
350
400
400
450
350
200
A) 900
B) 1200
C) 1100
D) 700
E) None of the above
Answer: D
Diff: 3
Topic: MINIMAL-SPANNING TREE PROBLEM
AACSB: Analytic Skills
57) Pipeline fluid flows are indicated below. Determine the maximum flow from Node 1 to Node 4.
From
Node
1
3
1
2
2
3
3
4
To
Node
3
1
2
1
3
2
4
3
Fluid
Flow
200
0
150
50
100
100
150
50
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A) 100
B) 150
C) 200
D) 50
E) None of the above
Answer: B
Diff: 3
Topic: MAXIMAL-FLOW PROBLEM
AACSB: Analytic Skills
58) Pipeline fluid flows are indicated below. Determine the maximum flow from Node 1 to Node 5.
From
Node
1
2
1
3
1
4
1
5
2
4
3
4
3
5
4
5
To
Node
2
1
3
1
4
1
5
1
4
2
4
3
5
3
5
4
Fluid
Flow
300
0
0
150
200
200
100
100
200
200
250
300
300
250
100
0
A) 300
B) 400
C) 600
D) 500
E) None of the above
Answer: D
Diff: 3
Topic: MAXIMAL-FLOW PROBLEM
AACSB: Analytic Skills
137
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59) Find the shortest route from Node 1 to Node 5 using the shortest-route technique.
From
Node
1
1
2
2
3
3
4
To
Node
2
3
3
4
4
5
5
Distance
200
150
50
300
250
200
150
A) 350
B) 400
C) 450
D) 600
E) None of the above
Answer: A
Diff: 3
Topic: SHORTEST-ROUTE PROBLEM
AACSB: Analytic Skills
60) Find the shortest route from Node 1 to Node 5.
From
Node
1
1
1
2
2
3
3
2
To
Node
2
3
4
3
4
4
5
5
Distance
250
150
200
50
150
150
100
150
A) 200
B) 350
C) 250
D) 450
E) None of the above
Answer: C
Diff: 3
Topic: SHORTEST-ROUTE PROBLEM
AACSB: Analytic Skills
138
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61) Find the shortest route from Node 1 to Node 6.
From
Node
1
1
2
2
2
3
3
4
5
To
Node
2
3
3
4
5
4
5
6
6
Distance
150
200
100
200
50
350
300
100
100
A) 300
B) 450
C) 550
D) 650
E) None of the above
Answer: A
Diff: 3
Topic: SHORTEST-ROUTE PROBLEM
AACSB: Analytic Skills
139
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62) Given the following traffic flows, in hundreds of cars per hour, what is the maximum traffic flow from City 1
to City 7?
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
From City
1
1
1
2
2
2
3
3
3
4
4
4
5
5
5
5
5
5
6
6
6
7
7
7
To City
2
3
5
1
4
5
1
5
6
2
5
7
1
2
3
4
6
7
3
5
7
4
5
6
Flow
4
8
5
0
3
3
0
3
1
3
3
4
1
0
2
0
1
5
1
4
1
2
1
0
A) 1200
B) 1400
C) 900
D) 800
E) None of the above
Answer: C
Diff: 3
Topic: MAXIMAL-FLOW PROBLEM
AACSB: Analytic Skills
140
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63) Solve the minimal-spanning tree problem defined below:
Branch
1
2
3
4
5
6
Start
Node
1
1
2
2
3
4
End
Node
3
2
4
5
4
6
Cost
5
1
3
4
6
2
A) total cost = 13
B) total cost = 15
C) total cost = 17
D) total cost = 11
E) None of the above
Answer: B
Diff: 3
Topic: MINIMAL-SPANNING TREE PROBLEM
AACSB: Analytic Skills
64) Find the shortest route from Node 1 to Node 6.
1
2
3
4
5
6
7
8
9
From
Node
1
1
2
2
2
3
4
4
5
To
Node
2
4
3
4
5
4
5
6
6
Distance
100
215
70
200
110
320
200
200
200
A) total distance = 350
B) total distance = 410
C) total distance = 270
D) total distance = 520
E) None of the above
Answer: B
Diff: 3
Topic: SHORTEST-ROUTE PROBLEM
AACSB: Analytic Skills
141
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65) Given the following traffic flows, in hundreds of cars per hour, what is the maximum traffic flow from Town 1
to Town 7?
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
From Town
1
1
1
2
2
2
3
3
3
4
4
4
5
5
5
5
5
5
6
6
6
7
7
7
To Town
2
3
5
1
4
5
1
5
6
2
5
7
1
2
3
4
6
7
3
5
7
4
5
6
Flow
4
7
9
0
3
5
1
3
4
3
1
0
1
0
3
0
5
1
1
6
3
5
2
0
A) max flow = 4 units
B) max flow = 6 units
C) max flow = 3 units
D) max flow = 9 units
E) None of the above
Answer: A
Diff: 3
Topic: MAXIMAL-FLOW PROBLEM
AACSB: Analytic Skills
142
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66) Find the shortest route from Node 6 to Node 1.
Branch
1
2
3
4
5
6
7
8
9
From
Node
1
1
2
2
2
3
3
4
5
To
Node
2
3
3
4
5
4
5
6
6
Distance
150
200
100
200
50
350
300
100
100
A) branches 9, 7, and 2
B) branches 8, 6, and 2
C) branches 8, 6, 7, and 1
D) branches 9, 5, and 1
E) None of the above
Answer: D
Diff: 3
Topic: SHORTEST-ROUTE PROBLEM
AACSB: Analytic Skills
143
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67) Given the pipeline fluid flows indicated below, determine the maximum flow from Node 1 to Node 5.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
From
Node
1
2
1
3
1
4
1
5
2
4
3
4
3
5
4
5
To
Node
2
1
3
1
4
1
5
1
4
2
4
3
5
3
5
4
Fluid
Flow
300
0
0
150
200
200
100
100
200
200
250
300
300
250
100
0
A) 250
B) 300
C) 350
D) 450
E) None of the above
Answer: E
Diff: 3
Topic: MAXIMAL-FLOW PROBLEM
AACSB: Analytic Skills
144
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68) Find the least amount of cable that will allow Jack's Cable Company to connect the following nodes (houses).
From
Node
1
1
1
2
2
3
To
Node
2
3
4
3
4
4
Distance
250
150
400
50
100
200
A) 250
B) 400
C) 350
D) 300
E) None of the above
Answer: D
Diff: 3
Topic: MINIMAL-SPANNING TREE PROBLEM
AACSB: Analytic Skills
69) Given the following nodes and distances, determine the minimum length of cable necessary to connect all six
nodes.
1
2
3
4
5
6
7
8
9
From
Node
1
1
2
2
2
3
3
4
5
To
Node
2
3
3
4
5
4
5
6
6
Distance
150
200
100
200
50
350
300
100
100
A) 200
B) 300
C) 400
D) 500
E) None of the above
Answer: D
Diff: 3
Topic: MINIMAL-SPANNING TREE PROBLEM
145
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AACSB: Analytic Skills
146
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70) Given the following nodes and distances, determine the minimal length of cable necessary to connect all
nodes, using Node 2 as the starting point.
1
2
3
4
5
6
7
8
9
10
From
1
1
1
2
2
3
3
4
4
5
To
2
3
5
3
4
4
5
5
6
6
Distance
200
300
400
300
400
200
200
100
300
400
A) 1200
B) 1100
C) 900
D) 700
E) None of the above
Answer: B
Diff: 3
Topic: MINIMAL-SPANNING TREE PROBLEM
AACSB: Analytic Skills
147
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71) Find the shortest route from Node 1 to each of the other nodes in the transportation network represented
below.
Route
from Node
1 to 2
1 to 3
2 to 3
2 to 4
3 to 4
3 to 5
4 to 5
4 to 6
5 to 6
Distance
50
100
75
65
80
70
65
200
130
Answer:
Node
2
3
4
5
6
Shortest
Route
1-2
1-3
1-2-4
1-3-5
1-2-4-5-6
Distance
50
100
115
170
310
Diff: 3
Topic: SHORTEST-ROUTE PROBLEM
AACSB: Analytic Skills
148
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72) As part of the planning for a major office development project, it is necessary to install telephone line to the
buildings. Information about the project is given below. The distances are provided in hundreds of feet. Which
offices should be connected so that total wiring costs (i.e., total distance) are minimized? What is the total length
of this?
Building
1 to 2
1 to 4
2 to 3
2 to 4
3 to 5
3 to 6
4 to 5
4 to 7
5 to 7
6 to 7
Distances (100s ft)
4
3
2
4
1
5
3
3
2
6
Answer: One solution is to connect 1-4, 2-3, 3-6, 3-5, 4-5, 5-7. Total length = 16.
Diff: 3
Topic: MINIMAL-SPANNING TREE PROBLEM
AACSB: Analytic Skills
73) A cable company must is to provide service for 7 houses in a particular neighborhood. They would like to
wire the neighborhood in a way to minimize the wiring costs (or distance). How should the cable company wire
the neighborhood and what would be the minimal length of the network?
House
1 to 2
1 to 3
1 to 4
2 to 3
2 to 4
2 to 5
3 to 5
3 to 6
4 to 5
4 to 7
5 to 7
6 to 7
Distances (yards)
100
400
300
300
250
400
350
450
300
250
100
150
Answer: One solution is to connect 1-2, 2-3, 2-4, 4-7, 5-7, 6-7. Total length = 1150.
Diff: 3
Topic: MINIMAL-SPANNING TREE PROBLEM
AACSB: Analytic Skills
149
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150
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74) Given a network with the following distances:
From
Node
1
1
2
2
3
3
3
4
5
To
Node
2
3
3
4
4
5
6
5
6
Distance
4
1
2
3
6
3
9
7
5
(a)
Determine which nodes should be connected to get the minimum distance from Nodes 1 through 6.
(b)
Determine the minimum distance.
Answer: (a) Connect 1-3-5-6.
(b) Minimum distance = 9
Diff: 3
Topic: SHORTEST-ROUTE PROBLEM
AACSB: Analytic Skills
75) The west-to-east air traffic system passing through the United States can handle aircraft flows with capacities
in hundreds of planes per hour as shown. What is the peak air traffic load (From City 1 to City 5) in aircraft per
hour that this system can handle?
Answer: Route 1235 can handle 200 per hour, and Route 145 can handle 300 per hour for a total of 500 aircraft per
hour.
Diff: 3
Topic: MAXIMAL-FLOW PROBLEM
AACSB: Analytic Skills
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76) Find the shortest route from Node 1 to each of the other nodes in the transportation network represented
below.
Route
From Node
1 to 2
1 to 3
2 to 3
2 to 5
3 to 4
3 to 5
3 to 6
4 to 6
5 to 6
Distance
50
100
75
60
80
70
65
200
150
Answer:
Node
2
3
4
5
6
Shortest
Route
1-2
1-3
1-3-4
1-2-5
1-3-6
Distance
50
100
180
110
165
Diff: 3
Topic: SHORTEST-ROUTE PROBLEM
AACSB: Analytic Skills
152
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77) A logistics company is determining the shortest route to get to a selected final destination. The information on
possible paths and distances is given below:
Route
From Node
1 to 2
1 to 3
1 to 4
2 to 4
2 to 5
3 to 4
3 to 5
4 to 5
4 to 6
5 to 6
5 to 7
6 to 7
Distance
50
100
125
75
180
100
125
170
200
125
100
75
Answer: 1-3-5-7 = 325
Diff: 3
Topic: SHORTEST-ROUTE PROBLEM
AACSB: Analytic Skills
78) As part of the planning for a major office development project, it is necessary to install telephone lines to the
buildings. Information about the project is given below. The distances are provided in hundreds of feet. Which
offices should be connected so that total wiring costs (i.e., total distance) are minimized? What is the total length
of this?
Buildings
1 to 2
1 to 3
1 to 4
2 to 4
3 to 5
3 to 6
4 to 5
4 to 7
5 to 7
6 to 7
Distances (100s ft)
4
3
2
4
1
5
3
3
2
6
Answer: Connect: 1-4, 4-5, 5-7, 3-6, 5-3, and either 4-2 or 1-2. Total length is 1700 feet. Alternate solutions exist.
Diff: 3
Topic: MINIMAL-SPANNING TREE PROBLEM
AACSB: Analytic Skills
153
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79) Brantley College has decided to "wire" its campus. The first stage in this effort is to install the "backbone," i.e.,
to connect all the buildings. The table below gives the distances between the various buildings on campus in
hundreds of feet. How should the buildings be connected to minimize the total length of cable? What length of
cable is required?
Answer: Connect: 1-2, 2-4, 4-6, 3-5, 5-6. Total length is 1600 feet.
Diff: 3
Topic: MINIMAL-SPANNING TREE PROBLEM
AACSB: Analytic Skills
80) Given a network with the following distances:
From
Node
1
1
2
2
3
3
3
4
4
5
5
6
To
Node
2
4
3
4
4
5
6
5
7
6
7
7
Distance
4
1
2
3
6
4
2
7
5
5
8
4
(a)
Determine which nodes should be connected to get the minimum distance flowing from Node 1 through
Node 7.
(b)
Determine the minimum distance.
Answer:
(a)
Connect: 1-4, 4-7.
(a)
Minimum distance = 6
Diff: 3
Topic: SHORTEST-ROUTE PROBLEM
154
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AACSB: Analytic Skills
155
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81) The east-to-west (City 5 to City 1) air traffic system passing through the U.S. can handle aircraft flows with
capacities in hundreds of planes per hour as shown. What is the peak air traffic load in aircraft per hour from
City 5 to City 1 that this system can handle?
Answer: 500 aircraft per hour.
Diff: 3
Topic: MAXIMAL-FLOW PROBLEM
AACSB: Analytic Skills
82) A water company is analyzing the flow of water through pipes in an office building. The flow capacities are
given in the table below. Flow is measured in 100 gallons/hour. What is the maximal flow of water from node 1
to node 5?
Answer: 700 gallons per hour.
Diff: 3
Topic: MAXIMAL-FLOW PROBLEM
AACSB: Analytic Skills
83) Describe the steps of the shortest-route technique.
Answer: (1) Find the nearest node to the origin (plant). Put the distance in a box by the node. (2) Find the nextnearest node to the origin (plant), and put the distance in a box by the node. In some cases, several paths will
have to be checked to find the nearest node. (3) Repeat this process until you have gone through the entire
network. The last distance at the ending node will be the distance of the shortest route. You should note that the
distance placed in the box by each node is the shortest route to this node. These distances are used as
intermediate results in finding the next-nearest node.
Diff: 3
Topic: SHORTEST-ROUTE PROBLEM
84) Briefly describe the minimal-spanning technique.
Answer: determines the path through a network that connects all the points while minimizing the total distance
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Diff: 2
Topic: INTRODUCTION
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85) Briefly describe the maximal-flow technique.
Answer: determines the maximal flow of any quantity or substance through a network
Diff: 2
Topic: INTRODUCTION
86) Briefly describe the minimal shortest-route technique.
Answer: determines the shortest route through a network
Diff: 2
Topic: INTRODUCTION
Quantitative Analysis for Management, 11e (Render)
Chapter 12 Project Management
1) PERT and CPM are quantitative analysis tools designed to schedule and control large projects.
Answer: TRUE
Diff: 1
Topic: INTRODUCTION
2) PERT is a deterministic analysis tool allowing for precise times of activities within a project.
Answer: FALSE
Diff: 2
Topic: INTRODUCTION
3) PERT had its beginnings in a military department of the United States.
Answer: TRUE
Diff: 2
Topic: PERT/CPM
4) CPM is a probabilistic analysis of managing a project.
Answer: FALSE
Diff: 2
Topic: INTRODUCTION
5) The first step in planning and scheduling a project is to develop the work breakdown structure.
Answer: TRUE
Diff: 2
Topic: INTRODUCTION
6) A PERT/CPM network is a graphical display of a project that connects activities.
Answer: TRUE
Diff: 1
Topic: PERT/CPM
7) The optimistic time is the greatest amount of time that could be required to complete an activity.
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Answer: FALSE
Diff: 2
Topic: PERT/CPM
8) PERT is a network technique similar to CPM, but PERT allows for project crashing, whereas CPM does not.
Answer: FALSE
Diff: 2
Topic: PERT/CPM and PROJECT CRASHING
9) In PERT, the most likely completion time of an activity is used to represent that activity's time within a project.
Answer: FALSE
Diff: 2
Topic: PERT/CPM
10) The expected completion time and variance of an activity is approximated by the normal distribution in a
PERT analysis.
Answer: FALSE
Diff: 2
Topic: PERT/CPM
11) PERT was developed for a project for which activity or task times were uncertain.
Answer: TRUE
Diff: 2
Topic: PERT/CPM
12) CPM was developed for use in managing projects about which we have good information about activity or
task completion times.
Answer: TRUE
Diff: 2
Topic: PERT/CPM
13) With PERT, we are able to calculate the probability of finishing the project within a specified time.
Answer: TRUE
Diff: 2
Topic: PERT/CPM
14) With CPM, we are able to calculate the probability of finishing the project within a specified time.
Answer: FALSE
Diff: 2
Topic: PERT/CPM
15) Both PERT and CPM networks show activities and activity sequences.
Answer: TRUE
Diff: 2
Topic: PERT/CPM
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16) The identification of the project activities and their time, cost, resource requirements, predecessors, and
person(s) responsible is called PERT planning.
Answer: FALSE
Diff: 2
Topic: INTRODUCTION
17) Before drawing a PERT or CPM network, we must identify all activities and their predecessors.
Answer: TRUE
Diff: 2
Topic: PERT/CPM
18) The three time estimates employed in PERT are optimistic time, average time, and pessimistic time.
Answer: FALSE
Diff: 2
Topic: PERT/CPM
160
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19) Given the variability of the activity completion times, the original critical path we identify in our PERT
analysis may not always be the actual critical path as the project takes place.
Answer: TRUE
Diff: 2
Topic: PERT/CPM
20) In PERT, the earliest start time for an activity is equal to the latest of the earliest finish times of all of its
immediate predecessors.
Answer: TRUE
Diff: 2
Topic: PERT/CPM
21) PERT stands for Probabilistic Evaluation and Review Technique.
Answer: FALSE
Diff: 3
Topic: INTRODUCTION
22) One of the most significant benefits of PERT is that it forces the project manager to sit down and plan the
project in great detail—and thus come to an understanding of relationships between the activities.
Answer: TRUE
Diff: 2
Topic: PERT/CPM
23) Slack is the time an activity can be delayed without impacting the completion time of the project.
Answer: TRUE
Diff: 2
Topic: PERT/CPM
24) The variance of the project completion time is equal to the sum of the variances of all the activities.
Answer: FALSE
Diff: 2
Topic: PERT/CPM
25) In PERT, we assume that the project completion time can be modeled by the normal distribution.
Answer: TRUE
Diff: 2
Topic: PERT/CPM
26) One PERT/COST assumption is that money is spent at a constant rate over the time taken to complete an
activity.
Answer: TRUE
Diff: 2
Topic: PERT/COST
27) CPM stands for Comprehensive Project Method.
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Answer: FALSE
Diff: 3
Topic: INTRODUCTION
162
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28) The longest time path through a PERT/CPM network is called the critical path.
Answer: TRUE
Diff: 2
Topic: INTRODUCTION
29) In CPM, crashing an activity that is not on the critical path increases the cost of the project.
Answer: TRUE
Diff: 2
Topic: PROJECT CRASHING
30) Through the use of PERT/CPM, astute managers can derive flexibility by identifying noncritical activities and
replanning, rescheduling, and reallocating resources such as personnel and finances.
Answer: TRUE
Diff: 2
Topic: INTRODUCTION
31) In PERT, the variance in completion time is equal to the variance of the most time consuming activity on the
critical path.
Answer: FALSE
Diff: 2
Topic: PERT/CPM
32) Given the assumptions in PERT, the probability that a project will be completed in less time than required by
the activities on the critical path is approximately 50%.
Answer: TRUE
Diff: 2
Topic: PERT/CPM
33) Gantt charts and PERT diagrams provide the same information, just in different formats.
Answer: FALSE
Diff: 2
Topic: PERT/CPM
34) Gantt charts contain information about the time taken by each activity, but not about the sequential
dependencies of the activities.
Answer: TRUE
Diff: 2
Topic: PERT/CPM
35) The critical path of a network is the
A) shortest time path through the network.
B) path with the fewest activities.
C) path with the most activities.
D) longest time path through the network.
E) None of the above
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Answer: D
Diff: 2
Topic: INTRODUCTION
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36) In a PERT network, the earliest (activity) start time is the
A) earliest time that an activity can be finished without delaying the entire project.
B) latest time that an activity can be started without delaying the entire project.
C) earliest time that an activity can start without violation of precedence requirements.
D) latest time that an activity can be finished without delaying the entire project.
E) None of the above
Answer: C
Diff: 1
Topic: PERT/CPM
37) Slack time in a network is the
A) amount of time that an activity would take assuming very unfavorable conditions.
B) shortest amount of time that could be required to complete the activity.
C) amount of time that you would expect it would take to complete the activity.
D) difference between the expected completion time of the project using pessimistic times and the expected
completion time of the project using optimistic times.
E) amount of time that an activity can be delayed without delaying the entire project.
Answer: E
Diff: 2
Topic: PERT/CPM
38) The first step in planning and scheduling a project is to develop the ________.
A) employee scheduling plan
B) PERT/CPM network diagram
C) critical path
D) work breakdown structure
E) variance calculations for each activity
Answer: D
Diff: 2
Topic: INTRODUCTION
39) Which of the following is not a concept associated with CPM?
A) normal time
B) probability
C) normal cost
D) crash cost
E) deterministic network
Answer: B
Diff: 2
Topic: INTRODUCTION
40) PERT
A) assumes that we do not know ahead of time what activities must be completed.
B) assumes that activity time estimates follow the normal probability distribution.
C) is a network technique that uses three time estimates for each activity in a project.
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D) is a deterministic network technique that allows for project crashing.
E) None of the above
Answer: C
Diff: 2
Topic: PERT/CPM
41) CPM
A) assumes we do not know ahead of time what activities must be completed.
B) assumes that activity time estimates follow the normal probability distribution.
C) is a deterministic network technique that allows for project crashing.
D) is a network technique that allows three time estimates for each activity in a project.
E) None of the above
Answer: C
Diff: 2
Topic: PERT/CPM
42) Managers use the network analysis of PERT and CPM to help them
A) derive flexibility by identifying noncritical activities.
B) replan, reschedule, and reallocate resources such as manpower and finances.
C) plan, schedule, monitor, and control large and complex projects.
D) All of the above
E) None of the above
Answer: D
Diff: 2
Topic: INTRODUCTION
43) The expected time in PERT is
A) a weighted average of the most optimistic time, most pessimistic time, and four times the most likely time.
B) the modal time of a beta distribution.
C) a simple average of the most optimistic, most likely, and most pessimistic times.
D) the square root of the sum of the variances of the activities on the critical path.
E) None of the above
Answer: A
Diff: 2
Topic: PERT/CPM
44) Given an activity's optimistic, most likely, and pessimistic time estimates of 4, 6, and 14 days respectively,
compute the PERT expected activity time for this activity.
A) 8
B) 6
C) 7
D) 9
E) None of the above
Answer: C
Diff: 2
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Topic: PERT/CPM
AACSB: Analytic Skills
167
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45) Given an activity's optimistic, most likely, and pessimistic time estimates of 2, 5, and 14 days respectively,
compute the PERT expected activity time for this activity.
A) 6
B) 7
C) 9
D) 5
E) None of the above
Answer: A
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
46) Given an activity's optimistic, most likely, and pessimistic time estimates of 4, 14, and 18 days respectively,
compute the PERT expected activity time for this activity.
A) 14
B) 12
C) 11
D) 13
E) None of the above
Answer: D
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
47) Given an activity's optimistic, most likely, and pessimistic time estimates of 2, 10, and 20 days respectively,
compute the PERT variance for this activity.
A) 3
B) 6
C) 9
D) 18
E) None of the above
Answer: C
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
48) Given an activity's optimistic, most likely, and pessimistic time estimates of 4, 12, and 18 days respectively,
compute the PERT variance for this activity.
A) 2.33
B) 5.44
C) 8.00
D) 64.00
E) None of the above
Answer: B
Diff: 2
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Topic: PERT/CPM
AACSB: Analytic Skills
169
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49) Given an activity's optimistic, most likely, and pessimistic time estimates of 3, 5, and 15 days, respectively,
compute the PERT standard deviation for this activity.
A) 2
B) 4
C) 5
D) 15
E) None of the above
Answer: A
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
50) Given the following small project, the critical path is ________ days.
Activity
A
B
C
Immediate
Predecessor
A, B
Time
(days)
10
4
6
A) 10
B) 14
C) 16
D) 20
E) None of the above
Answer: C
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
51) Given the following small project, the critical path is ________ days.
Activity
A
B
C
Immediate
Predecessor
A
-
Time
(days)
8
4
10
A) 4
B) 10
C) 12
D) 22
E) None of the above
Answer: C
Diff: 2
Topic: PERT/CPM
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AACSB: Analytic Skills
171
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Table 12-1
The following represents a project with know activity times. All times are in weeks.
Activity
A
B
C
D
E
F
Immediate
Predecessor
A
B
C, D
B
Time
4
3
2
7
4
5
52) Using the data in Table 12-1, what is the minimum possible time required for completing the project?
A) 8
B) 14
C) 25
D) 10
E) None of the above
Answer: B
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
53) Using the data in Table 12-1, what is the latest possible time that C may be started without delaying
completion of the project?
A) 0
B) 4
C) 8
D) 10
E) None of the above
Answer: C
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
54) According to Table 12-1, compute the slack time for activity D.
A) 0
B) 5
C) 3
D) 6
E) None of the above
Answer: A
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
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55) Using the data in Table 12-1, compute the latest finish time for activity E.
A) 4
B) 10
C) 14
D) 25
E) None of the above
Answer: C
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
Table 12-2
The following represents a project with four activities. All times are in weeks.
Activity
A
B
C
D
Immediate
Predecessor
A
B
Optimistic
Time
2
8
6
5
Most
Likely
Time
8
8
9
11
Pessimistic
Time
14
8
18
17
56) According to the data in Table 12-2, what is the critical path?
A) A-B
B) A-C
C) B-D
D) A-B-C-D
E) None of the above
Answer: C
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
57) According to the data in Table 12-2, what is the minimum expected completion time for the project?
A) 18
B) 19
C) 37
D) 11
E) None of the above
Answer: B
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
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58) According to Table 12-2, there are four activities in the project. Assume the normal distribution is appropriate
to use to determine the probability of finishing by a particular time. If you wished to find the probability of
finishing the project in 20 weeks or fewer, it would be necessary to find the variance and then the standard
deviation to be used with the normal distribution. What variance would be used?
A) 2
B) 4
C) 8
D) 12
E) None of the above
Answer: B
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
59) According to Table 12-2, there are four activities in the project. Assume the normal distribution is appropriate
to use to determine the probability of finishing by a particular time. What is the probability that the project is
finished in 16 weeks or fewer? (Round to two decimals.)
A) 0.07
B) 0.93
C) 0.43
D) 0.77
E) None of the above
Answer: A
Diff: 3
Topic: PERT/CPM
AACSB: Analytic Skills
60) Consider a project that has an expected completion time of 60 weeks and a standard deviation of five weeks.
What is the probability that the project is finished in 70 weeks or fewer? (Round to two decimals.)
A) 0.98
B) 0.48
C) 0.50
D) 0.02
E) 0.63
Answer: A
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
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61) Your company is considering submitting a bid on a major project. You determine that the expected
completion time is 100 weeks and the standard deviation is 10 weeks. It is assumed that the normal distribution
applies. You wish to set the due date for the project such that there is an 85 percent chance that the project will be
finished by this time. What due date should be set?
A) 108.0
B) 110.4
C) 89.6
D) 85.0
E) 100
Answer: B
Diff: 3
Topic: PERT/CPM
AACSB: Analytic Skills
Table 12-3
Activity
A
B
C
D
E
Immediate
Predecessor
--A
A
B, C
Optimistic
4
12
2
5
6
Most
Likely
5
16
8
5
7
Pessimistic
6
18
14
5
8
Standard
Deviation
0.333
1.000
2.000
0.000
0.333
Variance
0.111
1.000
4.000
0.000
0.111
62) According to Table 12-3, there are five activities in a PERT project. Which activities are on the critical path?
A) A-B-C-D-E
B) A-C-E
C) B-D
D) A-B-C-D
E) B-E
Answer: E
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
63) According to Table 12-3, there are five activities in a PERT project. What is the variance of the critical path?
A) 5.222
B) 4.222
C) 1.222
D) 0
E) 1.111
Answer: E
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
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64) According to Table 12-3, there are five activities in a PERT project. If the normal distribution were used to
find the probability of finishing this project in 24 weeks or fewer, what mean and variance would be used?
A) 20 and 4.222
B) 30 and 5.222
C) 20 and 5.222
D) 30 and 4.222
E) 22.667 and 1.111
Answer: E
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
65) The critical path of a network is the
A) path with the least variance.
B) path with zero slack.
C) path with the most activities.
D) path with the largest variance.
E) None of the above
Answer: B
Diff: 2
Topic: PERT/CPM
66) In a PERT network, the latest (activity) start time is the
A) earliest time that an activity can be finished without delaying the entire project.
B) latest time that an activity can be started without delaying the entire project.
C) earliest time that an activity can start without violation of precedence requirements.
D) latest time that an activity can be finished without delaying the entire project.
E) None of the above
Answer: B
Diff: 1
Topic: PERT/CPM
67) The work breakdown structure involves identifying the ________ for each activity.
A) time
B) cost
C) resource requirements
D) predecessors
E) All of the above
Answer: E
Diff: 2
Topic: INTRODUCTION
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68) PERT stands for ________.
A) probabilistic evaluation and review technique
B) program evaluation and review technique
C) probability of expected run times
D) program of expected run times
E) project evaluation and review technique
Answer: B
Diff: 2
Topic: INTRODUCTION
69) CPM stands for ________.
A) critical path management
B) critical project management
C) critical project method
D) critical path method
E) centralized project management
Answer: D
Diff: 2
Topic: INTRODUCTION
70) Which of the following questions can be answered by PERT?
A) When will the entire project be completed?
B) What is the probability that the project will be completed by a specific date?
C) What are the critical activities?
D) What are the noncritical activities?
E) All of the above
Answer: E
Diff: 1
Topic: PERT/CPM
71) In PERT, we assume that
A) the times to complete individual activities are known with certainty.
B) all activities are carried out by staff from our own organization.
C) the total cost of a project is independent of the time to complete the project.
D) the total time to complete all activities on the critical path is described by a normal distribution.
E) None of the above
Answer: D
Diff: 2
Topic: PERT/CPM
72) The two common techniques for drawing PERT networks are ________.
A) NOA and NRA
B) AON and AOA
C) GANTT and NOA
D) ONA and OAO
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E) CAN and CAA
Answer: B
Diff: 3
Topic: PERT/CPM
73) In PERT analysis, the probability of the optimistic time occurring should be on the order of ________.
A) 1/2
B) 1/3
C) 1/6
D) 1/10
E) 1/100
Answer: E
Diff: 2
Topic: PERT/CPM
74) The expected time in PERT is
A) greater than the most likely time.
B) equal to the most likely time.
C) less than the most likely time.
D) any of the above
E) None of the above
Answer: D
Diff: 2
Topic: PERT/CPM
75) Given an activity's optimistic, most likely, and pessimistic time estimates of 3, 7, and 11 days respectively,
compute the expected time for this activity.
A) 5
B) 6
C) 7
D) 12
E) None of the above
Answer: C
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
76) Given an activity's optimistic, most likely, and pessimistic time estimates of 3, 5, and 13 days respectively,
compute the expected time for this activity.
A) 3
B) 4
C) 5
D) 6
E) None of the above
Answer: D
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Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
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77) Given an activity's optimistic, most likely, and pessimistic time estimates of 1, 9, and 23 days respectively,
compute the PERT expected activity time for this activity.
A) 10
B) 12
C) 9
D) 11
E) None of the above
Answer: A
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
78) Given an activity's optimistic, most likely, and pessimistic time estimates of 3, 6, and 9 days respectively,
compute the PERT variance for this activity.
A) 3
B) 1
C) 9
D) 6
E) None of the above
Answer: B
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
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79) The project described by:
Activity
A
B
C
D
E
Immediate
Predecessor
-A
A
B
C
Time
(days)
10
4
6
7
5
is best represented by which of the following networks?
A)
B)
C)
D)
E) None of the above
Answer: A
Diff: 1
Topic: PERT/CPM
181
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AACSB: Analytic Skills
182
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80) The project described by:
Activity
A
B
C
D
E
Immediate
Predecessor
-A
A
B, C
C
Time
(days)
10
4
6
7
5
has a critical path of length of ________.
A) 21 days
B) 14 days
C) 23 days
D) 32 days
E) None of the above
Answer: C
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
81) The project described by:
Activity
A
B
C
D
E
Immediate
Predecessor
-A
-B, C
D
Time
(days)
6
2
8
5
7
has a critical path of length of ________.
A) 15 days
B) 20 days
C) 17 days
D) 18 days
E) None of the above
Answer: B
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
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Table 12-4
The following represents a project with known activity times. All times are in weeks.
Activity
A
B
C
D
E
F
G
Immediate
Predecessor
--A
B
C, D
B
E, F
Time
4
3
2
7
4
5
4
82) Using the data in Table 12-4, what is the minimum possible time required for completing the project?
A) 8
B) 12
C) 18
D) 10
E) None of the above
Answer: C
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
83) Using the data in Table 12-4, what is the latest possible time that C may be started without delaying
completion of the project?
A) 0
B) 4
C) 8
D) 10
E) None of the above
Answer: C
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
84) Using the data in Table 12-4, compute the slack time for activity D.
A) 0
B) 5
C) 3
D) 6
E) None of the above
Answer: A
Diff: 2
Topic: PERT/CPM
184
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AACSB: Analytic Skills
185
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85) Using the data in Table 12-4, compute the latest finish time for activity E.
A) 4
B) 10
C) 14
D) 25
E) None of the above
Answer: C
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
86) Using the data in Table 12-4, determine the latest time activity A can be started without delaying the project
completion.
A) 4
B) 3
C) 8
D) 6
E) None of the above
Answer: A
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
87) Using the data in Table 12-4, determine the latest time activity A can be finished and not delay any activity?
A) 4
B) 0
C) 8
D) 5
E) None of the above
Answer: C
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
88) Consider a project that has an expected completion time of 50 weeks and a standard deviation of 9 weeks.
What is the probability that the project is finished in 57 weeks or fewer? (Round to two decimals.)
A) 0.68
B) 0.78
C) 0.22
D) 0.32
E) None of the above
Answer: B
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
186
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89) Your company is considering submitting a bid on a major project. You determine that the expected
completion time is 150 weeks and the standard deviation is 10 weeks. It is assumed that the normal distribution
applies. You wish to set the due date for the project such that there is a 95 percent chance that the project will be
finished by this time. What due date should be set?
A) 108.0
B) 160.4
C) 166.5
D) 135.0
E) None of the above
Answer: C
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
Table 12-5
Activity
A
B
C
D
E
F
G
H
Immediate
Predecessor
--A
B
B
C, D
C, D
E, F
Time
4
5
3
8
2
3
7
2
ES
0
0
4
5
5
13
13
16
EF
4
5
7
13
7
16
20
18
LS
6
0
10
5
16
15
13
18
LF
10
5
13
13
18
18
20
20
90) How long could Table 12-5's activity E be delayed without delaying the completion of the project?
A) 7
B) 16
C) 11
D) 18
E) None of the above
Answer: C
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
91) How long could Table 12-5's activity F be delayed without delaying the project?
A) 2
B) 3
C) 14
D) 16
E) None of the above
Answer: A
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Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
92) What is the minimum possible time required for completing the Table 12-5 project?
A) 14
B) 18
C) 17
D) 20
E) None of the above
Answer: D
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
Table 12-6
Activity
A
B
C
D
E
F
G
H
Immediate
Predecessor
--A
A
B, C
B
D, E
G, F
Optimistic
2
2
1
5
6
14
1
1
Most
Likely
3
5
2
5
7
14
5
4
Pessimistic
4
8
9
5
8
14
9
8
σ
0.333
1.000
1.330
0.000
0.333
0.000
1.333
1.167
σ2
0.111
1.000
1.780
0.000
0.111
0.000
1.780
1.362
93) Which activities are part of Table 12-6's critical path?
A) A-B-E-G-H
B) A-C-E-G-H
C) A-D-G-H
D) B-F-H
E) None of the above
Answer: D
Diff: 3
Topic: PERT/CPM
AACSB: Analytic Skills
94) What is the variance of Table 12-6's critical path?
A) 5.222
B) 4.364
C) 1.362
D) 5.144
E) 2.362
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Answer: E
Diff: 3
Topic: PERT/CPM
AACSB: Analytic Skills
190
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Figure 12-1
95) Given the network in Figure 12-1, the critical path is
A) A-C-F-H.
B) B-D-E-F-H.
C) A-C-E-G-H.
D) B-D-G-E-F-H.
E) None of the above
Answer: B
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
96) Given the network in Figure 12-1, the time to complete those activities on the critical path is expected to be
________.
A) 20
B) 22
C) 25
D) 26
E) None of the above
Answer: C
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
97) Given the network shown in Figure 12-1, assume that completion of A is delayed by two days. What other
activities are impacted?
A) B
B) D
C) E
D) C
E) None of the above
Answer: D
Diff: 2
Topic: PERT/CPM
191
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AACSB: Analytic Skills
192
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98) Given the network shown in Figure 12-1, assume that completion of B is delayed by two days. What happens
to the project?
A) The critical path is extended by two days.
B) The start of activity F is delayed by two days.
C) The start of activity E is delayed by two days.
D) All of the above
E) None of the above
Answer: D
Diff: 2
Topic: PERT/CPM
99) Given the network shown in Figure 12-1, assume that the completion of activity C is delayed by four days.
What changes will take place?
A) The critical path will change to: A-C-B-D-E-F-H.
B) Activity F will be delayed by four days.
C) Activity E will be delayed by four days.
D) Activity G will be delayed by four days.
E) None of the above
Answer: E
Diff: 3
Topic: PERT/CPM
AACSB: Analytic Skills
100) Given the network shown in Figure 12-1 and the following information, what is the variance of the critical
path?
Activity
A
B
C
D
E
F
G
H
Expected time
3
5
6
4
5
4
6
7
Variance
2
3
3
1
1
2
2
2
A) 16
B) 7
C) 9
D) 8
E) None of the above
Answer: C
Diff: 3
Topic: PERT/CPM
AACSB: Analytic Skills
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101) PERT often assumes that time estimates follow which of the following probability distributions?
A) normal
B) exponential
C) binomial
D) Poisson
E) None of the above
Answer: E
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
102) PERT assumes that the total completion time of a projects follows which of the following probability
distributions?
A) normal
B) exponential
C) binomial
D) Poisson
E) None of the above
Answer: A
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
103) The crash time of an activity represents
A) the normal time to complete an activity.
B) the most pessimistic time to complete an activity.
C) the incremental decrease in the time to complete an activity.
D) the shortened activity time.
E) None of the above
Answer: D
Diff: 2
Topic: PROJECT CRASHING
104) Reducing the overall activity time is based on which of the following steps?
A) crashing activities with the lowest overall crash cost
B) crashing activities with the lowest overall normal cost
C) crashing activities on the critical path based on lowest overall cost
D) crashing activities on the critical path based on lowest cost/week
E) crashing activities with the lowest cost/week.
Answer: D
Diff: 2
Topic: PROJECT CRASHING
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105) An alternative approach to project crashing is to use which of the following techniques?
A) linear programming
B) nonlinear programming
C) Markov analysis
D) queuing theory
E) None of the above
Answer: A
Diff: 2
Topic: PROJECT CRASHING
106) Which of the following is not a decision variable when formulating the project crashing problem as a linear
program?
A) the early finish times of critical activities
B) the early finish times of non critical activities
C) the start time of the project
D) the finish time of the project
E) the early start times of all activities
Answer: E
Diff: 2
Topic: PROJECT CRASHING
107) Which of the following statement about project crashing is false?
A) The crash cost is greater than or equal to the normal cost of an activity.
B) The crash time is less than or equal to the normal time to complete an activity.
C) Reducing the time of an activity on the critical path automatically reduces total project duration.
D) It may not be possible to crash a particular activity.
E) Crashing may not lead to an overall reduction in costs for the project.
Answer: C
Diff: 3
Topic: PROJECT CRASHING
108) The process of smoothing out the utilization of resources in a project is called
A) CPM.
B) PERT.
C) project crashing.
D) work breakdown structure.
E) resource leveling.
Answer: E
Diff: 1
Topic: OTHER TOPICS IN PROJECT MANAGEMENT
195
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109) Consider the following project schedule:
Activity
A
B
C
D
E
F
G
H
Immediate
Predecessor
--A
B
B
C, D
C, D
E, F
Time
4
5
3
8
2
3
7
2
ES
0
0
4
5
5
13
13
16
EF
4
5
7
13
7
16
20
18
LS
6
0
10
5
16
15
13
18
LF
10
5
13
13
18
18
20
20
(a)
Which activities are critical?
(b)
Which activity has the most slack?
Answer: (a)
B, D, G
(b)
E
Diff: 1
Topic: PERT/CPM
AACSB: Analytic Skills
110) Consider the project with the following estimates for activity times and precedence relationships:
Activity
A
B
C
D
E
F
G
H
Optimistic
Time
3
5
2
2
1
3
7
2
Most
Likely Time
4
7
3
5
7
5
8
6
Pessimistic
Time
5
9
10
8
7
7
9
10
Immediate
Predecessor(s)
----A
B
B
C, D
D, E
F
(a)
What is the expected duration of the project?
(b)
What is the project variance?
(c)
If the deadline of the project is 25 days, what is the probability of finishing the project on time?
Answer:
(a)
23
(b)
3.67
(c)
0.8508
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
196
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111) Consider the tasks, durations, and predecessor relationships in the following network. Draw the network
and answer the questions that follow.
Activity
A
B
C
D
E
F
G
H
I
J
Immediate
Predecessors)
--A
A
B
D, C
C
F
F
E, G, H
I
Optimistic
(Weeks)
4
2
8
1
6
2
2
6
4
1
Most Likely
(Weeks)
7
8
12
2
8
3
2
8
8
2
Pessimistic
(Weeks)
10
20
16
3
22
4
2
10
12
3
(a) What is the expected duration of the project?
(b) What is the probability of completion of the project before week 42?
Answer:
(a) 40
(b) 8079
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
197
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112) Given:
Activity
A
B
C
D
E
F
G
Optimistic
3
6
6
0.5
2
4
1
Most
Likely
4
7
9
1
3
5
3
Pessimistic
5
14
12
1.5
10
12
11
Determine:
(a) the critical path.
(b) the probability that the project will be completed in 22 weeks.
Answer: (a) Critical path is A-C-F. Expected time is 19.
(b) Variance for critical path is 2.889, so standard deviation is 1.70. P(X ≤ 22) = 0.9608
Diff: 3
Topic: PERT/CPM
AACSB: Analytic Skills
198
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113) A small software development project has five major activities. The times are estimated and provided in the
table below.
Activity
A
B
C
D
E
Immediate
Predecessor
--A
B
C
a
2
10
4
2
3
m
5
10
7
5
3
b
8
10
10
14
3
(a) What is the expected completion time for this project?
(b) What variance would be used in finding probabilities of finishing by a certain time?
Answer:
(a) expected completion time = 16 (Activities B-D)
(b) variance = 0 + 4 = 4
Diff: 3
Topic: PERT/CPM
AACSB: Analytic Skills
199
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114) Development of a new deluxe version of a particular software product is being considered. The activities
necessary for the completion of this are listed in the table below (Time in weeks).
Activity
A
B
C
D
E
F
G
Normal
Time
4
2
3
8
6
3
4
Crash
Time
3
1
3
4
3
2
2
Normal
Cost
2200
2200
500
2300
900
3000
1400
Crash
Cost
2600
2800
500
2600
1200
4200
2000
Immediate
Predecessor
---A
B
C
D, E
(a) What is the project completion date?
(b) What is the total cost required for completing this project on normal time?
(c) If you wish to reduce the time required to complete this project by one week, which activity should be
crashed, and how much will this increase the total cost?
Answer:
(a) Project completion time = 16 weeks (Activities A-D-G)
(b) Total cost = $12,300
(c) Crash D, one week at an additional cost of $75
Diff: 3
Topic: PERT/CPM and PROJECT CRASHING
AACSB: Analytic Skills
200
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115) Draw the PERT network associated with the following activities.
Activity
A
B
C
D
E
F
G
H
I
J
Immediate
Predecessor
-A
A
B
B
C, E
A, D
F
F
G, H, I
Answer:
Diff: 2
Topic: PERT/CPM
AACSB: Analytic Skills
201
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116) Given (Time in weeks):
Activity
A
B
C
D
E
F
G
H
I
Optimistic
3
6
2
6
4
1
1
2
1
Most Likely
4
7
3
9
5
3
2
5
4
Pessimistic
5
14
10
12
12
11
9
8
7
Determine:
(a)
the critical path.
(b)
the probability that the project will be completed in 22 weeks.
Answer:
(a)
Critical path is B-E-G-I.
(b)
Variance for critical path is 6.33; standard deviation is 2.51. The probability that the project will be
completed in 22 weeks = 0.65.
Diff: 3
Topic: PERT/CPM
AACSB: Analytic Skills
202
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117) A small software development project has four major activities. The times are estimated and provided in the
table below.
Immediate
Activity Predecessor
A
-B
A
C
A
D
B
E
D
F
C
G
E, F
H
C
I
G, H
a
2
3
4
2
3
6
1
6
3
m
5
6
7
5
3
8
1
10
4
b
8
9
10
14
3
10
1
14
5
(a)
What is the expected completion time for this project?
(b)
What variance would be used in finding probabilities of finishing by a certain time?
Answer:
(a) expected completion time = 26 (Activities A-C-H-I)
(b) variance = 3.88
Diff: 3
Topic: PERT/CPM
AACSB: Analytic Skills
203
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118) Development of a new deluxe version of a particular software product is being considered. The activities
necessary for the completion of this are listed in the table below (Time in weeks).
Activity
A
B
C
D
E
F
G
H
I
Immediate
Predecessor
-A
A
B
D
C
E, F
C
G, H
a
m
b
2
3
4
2
3
6
1
6
3
5
6
7
5
3
8
1
10
4
8
9
10
14
3
10
1
14
5
(a)
If you wish to reduce the time required to complete this project by two weeks, which activity(ies) should
be crashed, and how much will this increase the total cost?
(b)
What would be the added cost if you wanted to complete the project in the minimum time possible?
Answer:
(a)
Crash D, two weeks at an additional cost of $100
(b)
Crash D 4 weeks, G 2 weeks, E 3 weeks, A 1 week, and B 1 week, for a total additional cost of $1,700
Diff: 3
Topic: PERT/CPM and PROJECT CRASHING
AACSB: Analytic Skills
119) PERT is the acronym for what?
Answer: Program Evaluation and Review Technique.
Diff: 2
Topic: INTRODUCTION
120) In a PERT analysis, how is the optimistic time defined?
Answer: the estimated time for an activity, should circumstances go as well as possible (should have a low
probability of actual occurrence)
Diff: 2
204
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Topic: PERT/CPM
205
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121) CPM is the acronym for what?
Answer: Critical Path Method
Diff: 2
Topic: INTRODUCTION
122) In PERT analysis, how is the pessimistic activity time defined?
Answer: the estimated time for an activity, based on unfavorable conditions (should have a low probability of
actual occurrence)
Diff: 2
Topic: PERT/CPM
123) In PERT/CPM, what is meant by the critical path?
Answer: the series of activities in a network that has zero slack or the longest time path through a network
Diff: 2
Topic: PERT/CPM
206
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97) Define infeasibility with respect to an LP solution.
Answer: This occurs when there is no solution that can satisfy all constraints simultaneously.
Diff: 2
Topic: FOUR SPECIAL CASES IN LP
98) Define unboundedness with respect to an LP solution.
Answer: This occurs when a linear program has no finite solution. The result implies that the formulation is
missing one or more crucial constraints.
Diff: 2
Topic: FOUR SPECIAL CASES IN LP
99) Define alternate optimal solutions with respect to an LP solution.
Answer: More than one optimal solution point exist because the objective function is parallel to a binding
constraint.
Diff: 2
Topic: FOUR SPECIAL CASES IN LP
100) How does the case of alternate optimal solutions, as a special case in linear programming, compare to the
two other special cases of infeasibility and unboundedness?
Answer: With multiple alternate solutions, any of those answers is correct. In the other two cases, no single
answer can be generated. Alternate solutions can occur when a problem is correctly formulated whereas the
other two cases most likely have an incorrect formulation.
Diff: 2
Topic: FOUR SPECIAL CASES IN LP
AACSB: Reflective Thinking
Quantitative Analysis for Management, 13e (Render et al.)
Chapter 13 Waiting Lines and Queuing Theory Models
33) Assume that we are using a waiting line model to analyze the number of service technicians required
to maintain machines in a factory. Our goal should be to
A) minimize the number of machines needing repair.
B) minimize the downtime for individual machines.
C) minimize the percent of idle time of the technicians.
D) minimize the total cost (cost of maintenance plus cost of downtime).
Answer: D
Diff: Moderate
Topic: WAITING LINE COSTS
LO: 12.1: Describe the trade-off curves for cost of waiting time and cost of service.
AACSB: Analytical thinking
Classification: Concept
34) In queuing analysis, total expected cost is the sum of expected ________ plus expected ________.
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A) service costs, arrival costs
B) facility costs, calling costs
C) calling costs, waiting costs
D) service costs, waiting costs
Answer: D
Diff: Easy
Topic: WAITING LINE COSTS
LO: 12.1: Describe the trade-off curves for cost of waiting time and cost of service.
AACSB: Analytical thinking
Classification: Concept
208
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35) In queuing theory, the calling population is another name for
A) the queue size.
B) the servers.
C) the arrivals.
D) the service rate.
Answer: C
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
36) An arrival in a queue that reneges is one who
A) after joining the queue, becomes impatient and leaves.
B) refuses to join the queue because it is too long.
C) goes through the queue, but never returns.
D) jumps from one queue to another, trying to get through as quickly as possible.
Answer: A
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
37) The customer who arrives at a bank, sees a long line, and leaves to return another time is
A) balking.
B) cropping.
C) reneging.
D) blithering.
Answer: A
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
209
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38) The customer who arrives at a bank, enters a line, and decides to leave is
A) balking.
B) cropping.
C) reneging.
D) blithering.
Answer: C
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
39) The three major characteristics of the input source that generates arrivals or customers for the
service system are
A) size, demographics, and behavior.
B) size, pattern, and behavior.
C) demographics, pattern, and behavior.
D) size, demographics, and pattern.
Answer: B
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
40) The term queue "discipline" describes the
A) degree to which members of the queue renege.
B) sequence in which members of the queue arrived.
C) degree to which members of the queue are orderly and quiet.
D) sequence in which members of the queue are serviced.
Answer: D
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
210
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41) A vendor selling newspapers on a street corner is an example of a
A) single-channel, multiphase system.
B) single-channel, single-phase system.
C) multichannel, multiphase system.
D) multichannel, single-phase system.
Answer: B
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
42) Lines at banks where customers wait for a teller window are usually representative of a
A) single-channel, multiphase system.
B) single-channel, single-phase system.
C) multichannel, multiphase system.
D) multichannel, single-phase system.
Answer: D
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
43) Which of the following distributions is most often used to estimate the arrival pattern?
A) negative exponential
B) normal
C) Poisson
D) Erlang
Answer: C
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
211
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44) A single automatic car wash with one bay and a cycle time of 2.5 minutes is what type of model?
A) M/M/1
B) M/M/2
C) M/D/2
D) M/D/1
Answer: D
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
45) A single automatic car wash with one bay and a service time that is normally distributed is what type
of model?
A) M/M/1
B) M/D/2
C) M/D/1
D) M/G/1
Answer: D
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
46) A suburban specialty restaurant has developed a single drive-thru window. Customers order, pay,
and pick up their food at the same window. Arrivals follow a Poisson distribution, while service times
follow an exponential distribution. What type of queuing model is exhibited in this problem?
A) M/M/1
B) M/M/2
C) M/D/2
D) M/D/1
Answer: D
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Concept
212
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47) A professor holds office hours during final exam week and discovers much to his dismay that his
sudden popularity affords him little time to engage in his favorite activity, watching cat videos. Fifteen
students per hour arrive at his office and he patiently answers questions, averaging three minutes per
student. If the average cat video is 60 seconds, how many videos can the professor watch in an hour?
A) 15
B) 18
C) 20
D) 24
Answer: A
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
48) A professor holds office hours during final exam week and discovers much to his dismay that his
sudden popularity affords him little time to engage in his favorite activity, watching cat videos. Fifteen
students per hour arrive at his office and he patiently answers questions, averaging three minutes per
student. On average, how many students are waiting to ask questions?
A) 2.00
B) 2.25
C) 2.50
D) 2.75
Answer: B
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
213
Copyright © 2012 Pearson Education, Inc. publishing as Prentice Hall
49) A professor holds office hours during final exam week and discovers much to his dismay that his
sudden popularity affords him little time to engage in his favorite activity, watching cat videos. Fifteen
students per hour arrive at his office and he patiently answers questions, averaging three minutes per
student. On average, how long must a student wait in line to get their last-minute questions answered?
A) 3 minutes
B) 6 minutes
C) 9 minutes
D) 12 minutes
Answer: C
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
50) A professor holds office hours during final exam week and discovers much to his dismay that his
sudden popularity affords him little time to engage in his favorite activity, watching cat videos. Fifteen
students per hour arrive at his office and he patiently answers questions, averaging three minutes per
student. A student joins the line at 9:45 am and the test is at 10:00 am the same morning. How much
time does the student have after getting his question answered to get to the exam room?
A) 12 minutes
B) 9 minutes
C) 6 minutes
D) 3 minutes
Answer: D
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
214
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51) Customers enter the waiting line at a cafeteria on a first-come, first-served basis. The arrival rate
follows a Poisson distribution, while service times follow an exponential distribution. If the average
number of arrivals is four per minute and the average service rate of a single server is seven per minute,
what is the average number of customers in the system?
A) 0.43
B) 1.67
C) 0.57
D) 1.33
Answer: D
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
52) Customers enter the waiting line at a cafeteria on a first-come, first-served basis. The arrival rate
follows a Poisson distribution, while service times follow an exponential distribution. If the average
number of arrivals is four per minute and the average service rate of a single server is seven per minute,
what is the average number of customers waiting in line behind the person being served?
A) 0.76
B) 0.19
C) 1.33
D) 1.67
Answer: A
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
215
Copyright © 2012 Pearson Education, Inc. publishing as Prentice Hall
53) Customers enter the waiting line to pay for food as they leave a cafeteria on a first-come, first-served
basis. The arrival rate follows a Poisson distribution, while service times follow an exponential
distribution. If the average number of arrivals is four per minute and the average service rate of a single
server is seven per minute, what proportion of the time is the server busy?
A) 0.43
B) 0.57
C) 0.75
D) 0.25
Answer: B
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
54) Customers enter the waiting line to pay for food as they leave a cafeteria on a first-come, first-served
basis. The arrival rate follows a Poisson distribution, while service times follow an exponential
distribution. If the average number of arrivals is four per minute and the average service rate of a single
server is seven per minute, on average, how much time will elapse from the time a customer enters the
line until he/she leaves the cafeteria?
A) 0.67 minute
B) 0.50 minute
C) 0.75 minute
D) 0.33 minute
Answer: D
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
216
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55) At a local fast-food joint, cars arrive randomly at a rate of 12 every 30 minutes. The fast food joint
takes an average of 2 minutes to serve each arrival. The utilization factor for this system is
A) 0.467.
B) 0.547.
C) 0.800.
D) 0.133.
Answer: C
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
56) At a local fast food joint, cars arrive randomly at a rate of 12 every 30 minutes. Service times are
random (exponential) and average 2 minutes per arrival. The average time in the queue for each arrival
is
A) 2 minutes.
B) 4 minutes.
C) 6 minutes.
D) 8 minutes.
Answer: D
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
57) Which of the following distributions is most often used to estimate service times?
A) negative exponential
B) normal
C) Poisson
D) Erlang
Answer: A
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
217
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58) Most systems use a queue discipline known as
A) shortest processing time.
B) longest processing time.
C) FIFO.
D) earliest due date.
Answer: C
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
59) A queuing system with a normally distributed arrival pattern, exponential service times, and three
servers would be described as
A) G/G/3.
B) M/M/3.
C) G/M/3.
D) M/G/3.
Answer: C
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
60) The initial state of a queuing system (for example, when a restaurant first opens), is referred to as the
________ state.
A) steady
B) primary
C) introductory
D) transient
Answer: D
Diff: Moderate
Topic: SOME GENERAL OPERATING CHARACTERISTIC RELATIONSHIPS
LO: 12.7: Understand Little's Flow Equations.
AACSB: Analytical thinking
Classification: Concept
218
Copyright © 2012 Pearson Education, Inc. publishing as Prentice Hall
61) A post office has a single line for customers waiting for the next available postal clerk. There are
two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson
distribution, while the service time follows an exponential distribution. What type of queuing model
applies here?
A) M/M/1
B) M/M/2
C) M/D/2
D) M/D/1
Answer: B
Diff: Easy
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
62) A post office has a single line for customers waiting for the next available postal clerk. There are
two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson
distribution, while the service time follows a normal distribution. What type of queuing model applies
here?
A) M/M/2
B) M/D/2
C) M/D/1
D) M/G/2
Answer: D
Diff: Easy
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
219
Copyright © 2012 Pearson Education, Inc. publishing as Prentice Hall
63) A post office has a single line for customers waiting for the next available postal clerk. There are
two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson
distribution, while the service time follows an exponential distribution. The average arrival rate is three
per minute and the average service rate is two per minute for each of the two clerks. What is the average
length of the line?
A) 3.429
B) 1.929
C) 1.143
D) 0.643
Answer: B
Diff: Difficult
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
64) A post office has a single line for customers waiting for the next available postal clerk. There are
two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson
distribution, while the service time follows an exponential distribution. The average arrival rate is three
per minute and the average service rate is two per minute for each of the two clerks. How long does the
average person spend waiting for a clerk?
A) 3.429 minutes
B) 1.929 minutes
C) 1.143 minutes
D) 0.643 minute
Answer: D
Diff: Difficult
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
220
Copyright © 2012 Pearson Education, Inc. publishing as Prentice Hall
65) A post office has a single line for customers waiting for the next available postal clerk. There are
two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson
distribution, while the service time follows an exponential distribution. The average arrival rate is three
per minute and the average service rate is two per minute for each of the two clerks. What proportion of
time are both clerks idle?
A) 0.643
B) 0.250
C) 0.750
D) 0.143
Answer: B
Diff: Difficult
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
Table 12-1
M/M/2
Mean Arrival Rate:
Mean Service Rate:
Number of Servers:
Server wage
Customer waiting cost
Probability of zero customers in system:
20 customers/hour
12 customers/hour
2
$10/hour
$20/hour
0.280
66) According to the information provided in Table 12-1, on average, how many customers are in the
line?
A) 3.79
B) 3.33
C) 4.25
D) 4.33
Answer: A
Diff: Moderate
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
221
Copyright © 2012 Pearson Education, Inc. publishing as Prentice Hall
67) According to the information provided in Table 12-1, how long does a customer wait on average?
A) 11 minutes
B) 11 minutes 30 seconds
C) 12 minutes 15 seconds
D) 12 minutes 45 seconds
Answer: B
Diff: Moderate
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
68) Using the information provided in Table 12-1, counting each person being served and the people in
line, on average, how many customers would be in this system?
A) 4.85
B) 5.05
C) 5.45
D) 6.15
Answer: C
Diff: Moderate
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
69) According to the information provided in Table 12-1, what is the hourly total cost of the system for
customers and servers? Assume that servers are paid only when they are helping customers.
A) $117.67
B) $121.47
C) $129.09
D) $125.76
Answer: D
Diff: Difficult
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
222
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70) According to the information provided in Table 12-1, what percentage of the total available service
time is being used?
A) 83.0%
B) 87.0%
C) 78.3%
D) 60.0%
Answer: A
Diff: Moderate
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
71) According to the information provided in Table 12-1, what is the average amount of time a customer
waits and is served?
A) 15 minutes 40 seconds
B) 16 minutes 20 seconds
C) 17 minutes
D) 17 minutes 40 seconds
Answer: B
Diff: Moderate
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
223
Copyright © 2012 Pearson Education, Inc. publishing as Prentice Hall
Table 12-2
M/M/2
Mean Arrival Rate:
Mean Service Rate:
Number of Servers:
5 occurrences per minute
3 occurrences per minute
2
Queue Statistics:
Mean Number of Units in the System:
Mean Number of Units in the Queue:
Mean Time in the System:
Mean Time in the Queue:
Service Facility Utilization Factor:
Probability in No Units in System:
5.455
3.788
1.091 minutes
0.758 minutes
0.833
0.091
72) According to the information provided in Table 12-2, which presents a queuing problem solution, on
average, how many units are in the line?
A) 5.455
B) 3.788
C) 1.091
D) 0.758
E) 0.833
Answer: B
Diff: Easy
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
73) According to the information provided in Table 12-2, which presents a queuing problem solution,
what proportion of time is at least one server busy?
A) 0.833
B) 0.758
C) 0.091
D) 0.909
Answer: D
Diff: Easy
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
224
Copyright © 2012 Pearson Education, Inc. publishing as Prentice Hall
Classification: Application
225
Copyright © 2012 Pearson Education, Inc. publishing as Prentice Hall
74) According to the information provided in Table 12-2, which presents a queuing problem solution,
there are two servers in this system. Counting each person being served and the people in line, on
average, how many people would be in this system?
A) 5.455
B) 3.788
C) 9.243
D) 10.900
Answer: A
Diff: Easy
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
Table 12-3
M/M/3
Mean Arrival Rate:
Mean Service Rate:
Number of Servers:
4 occurrences per minute
2 occurrences per minute
3
Queue Statistics:
Mean Number of Units in the System:
Mean Number of Units in the Queue:
Mean Time in the System:
Mean Time in the Queue:
Service Facility Utilization Factor:
Probability in No Units in System:
2.889
0.889
0.722 minutes
0.222 minutes
0.667
0.111
75) According to the information provided in Table 12-3, which presents a queuing problem solution,
what proportion of time is the system totally empty?
A) 0.111
B) 0.333
C) 0.889
D) 0.667
Answer: A
Diff: Easy
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
226
Copyright © 2012 Pearson Education, Inc. publishing as Prentice Hall
Classification: Application
227
Copyright © 2012 Pearson Education, Inc. publishing as Prentice Hall
76) According to the information provided in Table 12-3, which presents a queuing problem solution, on
average, how long does each customer spend waiting in line?
A) 0.333 minute
B) 0.889 minute
C) 0.222 minute
D) 0.722 minute
Answer: C
Diff: Easy
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
77) According to the information provided in Table 12-3, which presents a queuing problem solution,
what is the utilization rate of the service facility?
A) 0.889
B) 0.222
C) 0.722
D) 0.667
Answer: D
Diff: Easy
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
78) If everything else remains constant, including the mean arrival rate and service rate, except that the
service time becomes constant instead of exponential
A) the average queue length will be halved.
B) the average waiting time will be doubled.
C) the average queue length will be doubled.
D) There is not enough information to know what will happen to the queue length and waiting time.
Answer: A
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
228
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79) At an automatic car wash, cars arrive randomly at a rate of 7 cars every 30 minutes. The car wash
takes exactly 4 minutes (this is constant). On average, what would be the length of the line?
A) 8.171
B) 7.467
C) 6.53
D) 0.467
Answer: C
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
80) At an automatic car wash, cars arrive randomly at a rate of 7 every 30 minutes. The car wash takes
exactly 4 minutes (this is constant). On average, how long would each car spend at the car wash?
A) 28 minutes
B) 32 minutes
C) 17 minutes
D) 24 minutes
Answer: B
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
81) At an automatic car wash, cars arrive randomly at a rate of 7 every 30 minutes. The car wash takes
exactly 4 minutes (this is constant). On average, how long would each driver have to wait before
receiving service?
A) 28 minutes
B) 32 minutes
C) 17 minutes
D) 24 minutes
Answer: A
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
229
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82) At an automatic car wash, cars arrive randomly at a rate of 7 every 30 minutes. The car wash takes
exactly 4 minutes (this is constant). On average, how many customers would be at the car wash (waiting
in line or being serviced)?
A) 8.17
B) 7.46
C) 6.53
D) 0.46
Answer: B
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
83) At a local fast food joint, cars arrive randomly at a rate of 12 every 30 minutes. The fast food joint
takes exactly 2 minutes (this is constant). The average total time in the system is
A) 5.4 minutes.
B) 6.0 minutes.
C) 8.0 minutes.
D) 2.5 minutes.
Answer: B
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
230
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Table 12-4
The sentient car wash in Luther knows she is in for a busy day when dawn breaks on a gorgeous spring
morning. She is capable of washing a car every four minutes, and by the looks of things, it is reasonable
to expect a steady stream of twelve cars per hour arriving. Because she is fully automatic, she knows
that the four-minute estimate is accurate and invariant. She values her time at $10 per hour. Yes, it
seems low, but as a single bay car wash, there are few other jobs in town she is qualified for. (We won't
get into her unsuccessful turn at the beauty salon.) She estimates that customer time can be valued at $15
per hour.
84) According to the information provided in Table 12-4, how much time will the average customer
spend waiting in line?
A) 8 minutes
B) 9 minutes
C) 10 minute
D) 11 minute
Answer: A
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
85) According to the information provided in Table 12-4, on average, how many customers are in line?
A) 1.2 cars
B) 1.6 cars
C) 1.75 cars
D) 2.1 cars
Answer: B
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
231
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86) According to the information provided in Table 12-4, how many minutes per hour will the car wash
be idle and able to ponder the meaning of life?
A) 9 minutes
B) 10 minutes
C) 12 minutes
D) 15 minutes
Answer: C
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
87) According to Table 12-4, what is the total hourly cost of the system for customers and the car wash
herself? Assume the car wash is paid only when she is washing cars.
A) $38
B) $40
C) $42
D) $44
Answer: D
Diff: Difficult
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
88) According to Table 12-4, what is the total number of cars in the system?
A) 2.40
B) 2.75
C) 3.10
D) 3.45
Answer: A
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
232
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Table 12-5
M/D/1
Mean Arrival Rate:
Constant Service Rate:
5 occurrences per minute
7 occurrences per minute
Queue Statistics:
Mean Number of Units in the System:
Mean Number of Units in the Queue:
Mean Time in the System:
Mean Time in the Queue:
Service Facility Utilization Factor:
1.607
0.893
0.321 minutes
0.179 minutes
0.714
89) According to the information provided in Table 12-5, which presents the solution for a queuing
problem with a constant service rate, on average, how much time is spent waiting in line?
A) 1.607 minutes
B) 0.714 minute
C) 0.179 minute
D) 0.893 minute
Answer: C
Diff: Easy
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
90) According to the information provided in Table 12-5, which presents the solution for a queuing
problem with a constant service rate, on average, how many customers are in the system?
A) 0.893
B) 0.714
C) 1.607
D) 0.375
Answer: C
Diff: Easy
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
233
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91) According to the information provided in Table 12-5, which presents a queuing problem solution for
a queuing problem with a constant service rate, on average, how many customers arrive per time period?
A) 5
B) 7
C) 1.607
D) 0.893
Answer: A
Diff: Easy
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
92) According to the information provided in Table 12-5, which presents the solution for a queuing
problem with a constant service rate, on average, how many minutes does a customer spend in the
system?
A) 0.893 minute
B) 0.321 minute
C) 0.714 minute
D) 1.607 minutes
Answer: B
Diff: Easy
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
93) According to the information provided in Table 12-5, which presents the solution for a queuing
problem with a constant service rate, the probability that the server is idle is
A) 0.217.
B) 0.643.
C) 0.286.
D) 0.714.
Answer: C
Diff: Easy
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
234
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94) Thanks to a generous and eccentric donor, the school of business has 3 fax machines. The toner in
each machine needs to be changed after about 5 hours of use. There is one unit secretary who is
responsible for the fax machine maintenance. It takes him 15 minutes to replace the toner cartridge.
What is the probability that none of the fax machines need toner?
A) 1.1500
B) 1.1658
C) .8578
D) .7696
Answer: C
Diff: Difficult
Topic: FINITE POPULATION MODEL (M/M/1 WITH FINITE SOURCE)
LO: 12.6: Analyze a variety of operating characteristics of waiting lines for single channel model with
exponential service times and finite calling populations.
AACSB: Analytical thinking
Classification: Application
95) Thanks to a generous and eccentric donor, the school of business has 3 fax machines. The toner in
each machine needs to be changed after about 5 hours of use. There is one unit secretary who is
responsible for the fax machine maintenance. It takes him 15 minutes to replace the toner cartridge.
What is the average number of fax machines in the queue?
A) 0.5658 fax machines
B) 0.3304 fax machines
C) .0563 fax machine
D) .0142 fax machine
Answer: D
Diff: Difficult
Topic: FINITE POPULATION MODEL (M/M/1 WITH FINITE SOURCE)
LO: 12.6: Analyze a variety of operating characteristics of waiting lines for single channel model with
exponential service times and finite calling populations.
AACSB: Analytical thinking
Classification: Application
96) Thanks to a generous and eccentric donor, the school of business has 3 fax machines. The toner in
each machine needs to be changed after about 5 hours of use. There is one unit secretary who is
responsible for the fax machine maintenance. It takes him 15 minutes to replace the toner cartridge.
What is the average number of fax machines in the system?
A) .0142 fax machine
B) .1563 fax machine
C) .0249 fax machine
D) .2749 fax machine
Answer: B
Diff: Difficult
Topic: FINITE POPULATION MODEL (M/M/1 WITH FINITE SOURCE)
LO: 12.6: Analyze a variety of operating characteristics of waiting lines for single channel model with
235
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exponential service times and finite calling populations.
AACSB: Analytical thinking
Classification: Application
97) Thanks to a generous and eccentric donor, the school of business has 3 fax machines. The toner in
each machine needs to be changed after about 5 hours of use. There is one unit secretary who is
responsible for the fax machine maintenance. It takes him 15 minutes to replace the toner cartridge.
What is the average waiting time in the queue?
A) .0142 hour
B) .1563 hour
C) .0249 hour
D) .2749 hour
Answer: C
Diff: Difficult
Topic: FINITE POPULATION MODEL (M/M/1 WITH FINITE SOURCE)
LO: 12.6: Analyze a variety of operating characteristics of waiting lines for single channel model with
exponential service times and finite calling populations.
AACSB: Analytical thinking
Classification: Application
98) Thanks to a generous and eccentric donor, the school of business has 3 fax machines. The toner in
each machine needs to be changed after about 5 hours of use. There is one unit secretary who is
responsible for the fax machine maintenance. It takes him 15 minutes to replace the toner cartridge.
What is the probability that one of the fax machines needs toner?
A) 0.22
B) 0.19
C) 0.16
D) 0.13
Answer: D
Diff: Difficult
Topic: FINITE POPULATION MODEL (M/M/1 WITH FINITE SOURCE)
LO: 12.6: Analyze a variety of operating characteristics of waiting lines for single channel model with
exponential service times and finite calling populations.
AACSB: Analytical thinking
Classification: Application
236
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Table 12-6
Customers arrive at coffee shop at a rate of 40 per hour. There are 2 servers available and it takes an
average of 1 minute to serve each customer.
99) Using Table 12-6, what proportion of time are the servers busy?
A) 0
B) 0.333
C) 0.5
D) 0.6667
Answer: B
Diff: Moderate
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
100) Using Table 12-6, what is the probability of no customers in the system?
A) 0
B) 0.333
C) 0.5
D) 0.667
Answer: C
Diff: Moderate
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
101) Using Table 12-6, what is the average number of customers in the coffee shop?
A) 0.0833
B) 0.5
C) 0.75
D) 1.33
Answer: C
Diff: Moderate
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
237
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AACSB: Analytical thinking
Classification: Application
102) Using Table 12-6, what is the average number of customers waiting in line?
A) 0.0833
B) 0.5
C) 0.75
D) 1.33
Answer: A
Diff: Moderate
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
103) The school of business has 3 fax machines. The toner in each machine needs to be changed after
about 5 hours of use. There is one unit secretary who is responsible for the fax machine maintenance. It
takes him 15 minutes to replace the toner cartridge. What is the average time spent in the system?
A) .0142 hour
B) .1563 hour
C) .0249 hour
D) .2749 hour
Answer: D
Diff: Difficult
Topic: FINITE POPULATION MODEL (M/M/1 WITH FINITE SOURCE)
LO: 12.6: Analyze a variety of operating characteristics of waiting lines for single channel model with
exponential service times and finite calling populations.
AACSB: Analytical thinking
Classification: Application
104) The school of business has 3 fax machines. The toner in each machine needs to be changed after
about 5 hours of use. There is one unit secretary who is responsible for the fax machine maintenance. It
takes him 15 minutes to replace the toner cartridge. What is the probability that 2 fax machines need
toner at the same time?
A) .8576
B) .1286
C) .0129
D) .1415
Answer: C
Diff: Difficult
Topic: FINITE POPULATION MODEL (M/M/1 WITH FINITE SOURCE)
LO: 12.6: Analyze a variety of operating characteristics of waiting lines for single channel model with
238
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exponential service times and finite calling populations.
AACSB: Analytical thinking
Classification: Application
239
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105) A new shopping mall is considering setting up an information desk manned by one employee.
Based upon information obtained from similar information desks, it is believed that people will arrive at
the desk at the rate of 15 per hour. It takes an average of two minutes to answer a question. It is assumed
that arrivals are Poisson and answer times are exponentially distributed.
(a) Find the probability that the employee is idle.
(b) Find the proportion of time that the employee is busy.
(c) Find the average number of people receiving and waiting to receive information.
(d) Find the average number of people waiting in line to get information.
(e) Find the average time a person seeking information spends at the desk.
(f) Find the expected time a person spends waiting in line to have his question answered.
Answer:
(a) Po = 0.50
(b) ρ = 0.50
(c) L = 1
(d) Lq = 0.50
(e) W = 0.0667 hour
(f) Wq = 0.0333 hour
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
240
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106) A new shopping mall is considering setting up an information desk manned by one employee.
Based upon information obtained from similar information desks, it is believed that people will arrive at
the desk at the rate of 15 per hour. It takes exactly two minutes to answer each question. It is assumed
that arrivals are Poisson.
(a) Find the probability that the employee is idle.
(b) Find the proportion of time that the employee is busy.
(c) Find the average number of people receiving and waiting to receive information.
(d) Find the average number of people waiting in line to get information.
(e) Find the average time a person seeking information spends at the desk.
(f) Find the expected time a person spends waiting in line to have his question answered.
Answer:
(a) Po = 0.50
(b) ρ = 0.50
(c) L = 0.75
(d) Lq = 0.25
(e) W = 0.05 hour
(f) Wq = 0.03 hour
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
241
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107) Sam the Vet is running a rabies vaccination clinic for dogs at the local grade school. Sam can
vaccinate a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly
throughout the day at a rate of 1 dog every 6 minutes, according to a Poisson distribution. Also assume
that Sam's vaccinating times are exponentially distributed.
(a) Find the probability that Sam is idle.
(b) Find the proportion of time that Sam is busy.
(c) Find the average number of dogs receiving or waiting to be vaccinated.
(d) Find the average number of dogs waiting to be vaccinated.
(e) Find the average time a dog waits before getting vaccinated.
(f) Find the average amount (mean) of time a dog spends between waiting in line and getting vaccinated.
Answer:
(a) Po = 0.5
(b) ρ = 0.5
(c) L = 1
(d) Lq = 0.5
(e) Wq = 0.05 hour
(f) W = 0.1 hour
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
242
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108) Sam the Vet is running a rabies vaccination clinic for dogs at the local grade school. Sam can
vaccinate a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly
throughout the day at a rate of 1 dog every 4 minutes, according to a Poisson distribution. Also assume
that Sam's vaccinating times are exponentially distributed.
(a) Find the probability that Sam is idle.
(b) Find the proportion of time that Sam is busy.
(c) Find the average number of dogs receiving or waiting to be vaccinated.
(d) Find the average number of dogs waiting to be vaccinated.
(e) Find the average time a dog waits before getting vaccinated.
(f) Find the average amount (mean) of time a dog spends between waiting in line and getting vaccinated.
Answer: a. Po = 0.25
b. ρ = 0.75
c. L = 3
d. Lq = 2.25
e. Wq = 0.15 hour
f. W = 0.2 hour
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
109) A dry cleaner has a single drive-thru window for customers. The arrival rate of cars follows a
Poisson distribution, while the service time follows an exponential distribution. The average arrival rate
is 16 per hour and the average service time is three minutes.
(a) What is the average number of cars in the line?
(b) What is the average time spent waiting to get to the service window?
(c) What percentage of time is the dry cleaner's drive-thru window idle?
(d) What is the probability there are more than 2 cars at the drive-thru window?
Answer:
(a) Lq = 3.2
(b) Wq = 0.2 hour (12 minutes)
(c) Po = 0.20
(d) Pn > k = 0.512
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
243
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110) A dry cleaner has a single drive-thru window for customers. The arrival rate of cars follows a
Poisson distribution, while the service time follows an exponential distribution. The average arrival rate
is 16 per hour and the average service time is three minutes. If the dry cleaner wants to accommodate
(have enough room for) all of the waiting cars at least 96 percent of the time, how many car-lengths
should they make the driveway leading to the window?
Answer: The probability of having more than 14 cars in the system is (16/20)14 + 1 = 0.035, so they
should make the driveway approximately 13 car-lengths long (because one car will be at the service
window). (The probability of having more than 13 cars in the system is 0.044 (which is too high), and
the percentage only gets worse as the queue length is shortened.)
Diff: Difficult
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
111) Sam the Vet is running a rabies vaccination clinic for dogs at the local grade school. Sam can
vaccinate a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly
throughout the day at a rate of 1 dog every 6 minutes, according to a Poisson distribution. Also assume
that Sam's vaccinating times are exponentially distributed. Sam would like to have each waiting dog
placed in a holding pen. If Sam wants to be certain he has enough cages to accommodate all dogs at
least 90 percent of the time, how many cages should he prepare?
Answer: He needs to prepare 2 cages. The probability of having more than 3 dogs in the system is
0.0625 while the probability of having more than 2 dogs in the system is 0.125.
Diff: Difficult
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
244
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112) A new shopping mall is considering setting up an information desk operated by two employees.
Based on information obtained from similar information desks, it is believed that people will arrive at
the desk at the rate of 20 per hour. It takes an average of 4 minutes to answer a question. It is assumed
that arrivals are Poisson and answer times are exponentially distributed.
(a) Find the proportion of the time that the employees are busy.
(b) Find the average number of people waiting in line to get some information.
(c) Find the expected time a person spends just waiting in line to have his question answered.
Answer:
(a) ρ = 0.667
(b) Lq = 1.0667
(c) Wq = 0.0533 hour
Diff: Difficult
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
113) Cars arrive at a parking lot entrance at the rate of 20 per hour. The average time to get a ticket and
proceed to a parking space is two minutes. There are two lot attendants at the current time. The Poisson
and exponential distribution appear to be relevant in this situation.
(a) What is the probability that an approaching auto must wait?
(b) What is the average waiting time?
(c) What is the average number of autos waiting to enter the garage?
Answer:
(a) Po = 0.50
(b) Wq = 0.25 minute
(c) Lq = 0.0833 auto
Diff: Difficult
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
245
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114) Bank Boston has a branch at Bryant College. The branch is busiest at the beginning of the college
year when freshmen and transfer students open accounts. This year, freshmen arrived at the office at a
rate of 40 per day (8-hour day). On average, it takes the Bank Boston staff person about ten minutes to
process each account application. The bank is considering having one or two tellers. Each teller is paid
$12 per hour and the cost of waiting in line is assumed to be $8 per hour.
(a) What is the total daily waiting cost for the single teller model?
(b) What is the total daily waiting cost for the two-teller model?
(c) What is the total daily service cost for the single teller model?
(d) What is the total daily service cost for the two-teller model?
(e) Which model is preferred?
Answer:
(a) Total wait cost = [(5 * .833 hours) (8)] * 8 hours/day = $266.56
(b) Total wait cost = [(5 * .035 hours) (8)] * 8 hours/day = $11.20
(c) Total service cost = (1 * $12) * 8 hours/day = $96
(d) Total service cost = (2 * $12) * 8 hours/day = $192
(e) Two channel model
Diff: Difficult
Topic: VARIOUS
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations. 12.4: Analyze a variety of operating
characteristics of waiting lines for multi-channel models with exponential service times and infinite
calling populations.
AACSB: Analytical thinking
Classification: Application
246
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115) At the start of football season, the ticket office gets busy the day before the first game. Customers
arrive at the rate of four every ten minutes. A ticket seller can service a customer in four minutes.
Traditionally, there are two ticket sellers working. The university is considering an automated ticket
machine similar to the airlines' e-ticket system. The automated ticket machine can service a customer in
2 minutes.
(a) What is the average length of the queue for the in-person model?
(b) What is the average length of the queue for the automated system model?
(c) What is the average time in the system for the in-person model?
(d) What is the average time in the system for the automated system model?
(e) Assume the ticket sellers earn $8 per hour and the machine costs $20 per hour (amortized over 5
years). The wait time is only $4 per hour because students are patient. What is the total cost of each
model?
Answer:
(a) Lq = 2.844
(b) Lq = 1.6
(c) W = 0.1852 hour or 11.11 minutes
(d) W = 0.1 hour or 6 minutes
(e) Total cost (in-person) = (2 ∗ $8/hour) + (24/hour ∗ .1852 hours) ($4/hour) = $33.78
Total cost (automated) = (1 ∗ $20/hour) + (24/hour ∗ .1 hour) ($4/hour) = $29.60
Diff: Difficult
Topic: VARIOUS
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations. 12.5 Analyze a variety of operating
characteristics of waiting lines for single channel models with deterministic service times and infinite
calling populations.
AACSB: Analytical thinking
Classification: Application
116) Consider a single-server queuing system with Poisson arrivals of 10 units per hour and a constant
service time of 2 minutes per unit. How long will the customer waiting time be in seconds, on average?
Answer: 10 / [(2)(30)(30 − 10)] = .00833333 hours = 0.5 minute = 30 seconds
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
247
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117) There is a tutoring lab at a university that holds 20 students. Due to the popularity of the 3 tutors,
the lab is always at capacity. Each student approaches a tutor an average of 2 times per hour, and a tutor
spends on average 5 minutes per question from a student. The service time follows an exponential
distribution.
(a) What proportion of the time are the tutors busy?
(b) What is the average waiting time for students in queue?
Answer:
(a) ρ = 0.86
(b) Wq = 0.06 hour
Diff: Moderate
Topic: FINITE POPULATION MODEL (M/M/1 WITH FINITE SOURCE)
LO: 12.6: Analyze a variety of operating characteristics of waiting lines for single channel model with
exponential service times and finite calling populations.
AACSB: Analytical thinking
Classification: Application
118) A professor decides to hold a three-hour window open for student advising. The professor has 15
advisees. He's unsure if each advisee will show up, and it's possible that a single advisee could show up
multiple times during the 3-hour window. On average, the professor will spend 12 minutes with each
student. He usually expects each student to arrive once during the 3-hour window.
(a) What proportion of the time can the professor expect to be busy during the window?
(b) What is the expected number of students in queue during the window?
(c) What is the expected wait time in queue during the window?
Answer:
(a) ρ = 0.82
(b) Lq = 1.88
(c) Wq = 0.46 hour
Diff: Difficult
Topic: FINITE POPULATION MODEL (M/M/1 WITH FINITE SOURCE)
LO: 12.6: Analyze a variety of operating characteristics of waiting lines for single channel model with
exponential service times and finite calling populations.
AACSB: Analytical thinking
Classification: Application
248
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119) Customers arrive at a bank at a rate of one every minute. The bank has 3 tellers and on average, it
takes two minutes to service a customer.
(a) What proportion of time are the tellers busy?
(b) What is the average number of customers in the bank?
(c) What is the average weight time?
Answer:
(a) ρ = 0.67
(b) L = 2.89
(c) Wq = 0.01 hour = 0.89 minutes = 53.33 seconds
Diff: Difficult
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
120) Customers arrive at their friendly DMV at a rate of 45 people per hour. There are four servers that
can process customers at an average of 3 minutes.
(a) What is the average wait time?
(b) What is the average number of customers waiting?
(c) What is the average number of customers in the DMV?
Answer:
(a) Wq = 0.01 hours = .41 minutes = 24.81 seconds
(b) Lq = 0.31 customers
(c) L = 2.56
Diff: Difficult
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
121) What is meant by a single-channel queuing system?
Answer: one service facility system fed by one queue
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
249
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122) What is meant by a multichannel queuing system?
Answer: more than one service facility all fed by the same queue
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
123) What is meant by a single-phase system?
Answer: Arrivals leave the system after receiving service at only one station.
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
124) What is meant by a multiphase system?
Answer: Service is provided at more than one station, one after the other.
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
125) What is the difference between customers balking and customers reneging? If you managed a retail
store how would you track and differentiate between customers that balked and reneged?
Answer: Balking occurs when customers decline to join the queue, typically because they see the line is
too long and they don't have enough time. Reneging occurs when customers join the queue and change
their mind later and depart the queue. Answers will vary as to how they can be tracked. It may be easier
to track those that renege if some part of the service process has already begun and customer
information is recorded. Alternatively, security camera footage could be checked at the end of each day
to see the number that joined a line and then left. Balking would probably be tougher to capture in most
situations.
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
250
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126) What is the difference between a transient state and a steady state? How could you as a manager
distinguish between the two?
Answer: A steady state is the normal operating condition of the queuing system. A queuing system is in
a transient state before the steady state is reached. A manager would expect to be in a transient state at
opening time each day or after a holiday and be in steady state during most operating hours if most
queuing analysis assumptions are reasonable. For pure customer service situations, there may be
additional transient periods of the day, for example, a lunch or dinner rush at a restaurant.
Diff: Moderate
Topic: SOME GENERAL OPERATING CHARACTERISTIC RELATIONSHIPS
LO: 12.7: Understand Little's Flow Equations.
AACSB: Analytical thinking
Classification: Concept
127) Four thousand students are admitted each year at a large regional university. The average time to
complete a degree is six years and the university's retention rate initiative achieves 100% (no students
drop out or transfer). What is the student population?
Answer: 24,000 students; L = λW = 4000 students/year × 6 years
Diff: Easy
Topic: SOME GENERAL OPERATING CHARACTERISTIC RELATIONSHIPS
LO: 12.7: Understand Little's Flow Equations.
AACSB: Analytical thinking
Quantitative Analysis for Management, 13e (Render et al.)
Chapter 13 Waiting Lines and Queuing Theory Models
33) Assume that we are using a waiting line model to analyze the number of service technicians required
to maintain machines in a factory. Our goal should be to
A) minimize the number of machines needing repair.
B) minimize the downtime for individual machines.
C) minimize the percent of idle time of the technicians.
D) minimize the total cost (cost of maintenance plus cost of downtime).
Answer: D
Diff: Moderate
Topic: WAITING LINE COSTS
LO: 12.1: Describe the trade-off curves for cost of waiting time and cost of service.
AACSB: Analytical thinking
Classification: Concept
34) In queuing analysis, total expected cost is the sum of expected ________ plus expected ________.
A) service costs, arrival costs
B) facility costs, calling costs
C) calling costs, waiting costs
D) service costs, waiting costs
251
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Answer: D
Diff: Easy
Topic: WAITING LINE COSTS
LO: 12.1: Describe the trade-off curves for cost of waiting time and cost of service.
AACSB: Analytical thinking
Classification: Concept
252
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35) In queuing theory, the calling population is another name for
A) the queue size.
B) the servers.
C) the arrivals.
D) the service rate.
Answer: C
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
36) An arrival in a queue that reneges is one who
A) after joining the queue, becomes impatient and leaves.
B) refuses to join the queue because it is too long.
C) goes through the queue, but never returns.
D) jumps from one queue to another, trying to get through as quickly as possible.
Answer: A
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
37) The customer who arrives at a bank, sees a long line, and leaves to return another time is
A) balking.
B) cropping.
C) reneging.
D) blithering.
Answer: A
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
253
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38) The customer who arrives at a bank, enters a line, and decides to leave is
A) balking.
B) cropping.
C) reneging.
D) blithering.
Answer: C
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
39) The three major characteristics of the input source that generates arrivals or customers for the
service system are
A) size, demographics, and behavior.
B) size, pattern, and behavior.
C) demographics, pattern, and behavior.
D) size, demographics, and pattern.
Answer: B
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
40) The term queue "discipline" describes the
A) degree to which members of the queue renege.
B) sequence in which members of the queue arrived.
C) degree to which members of the queue are orderly and quiet.
D) sequence in which members of the queue are serviced.
Answer: D
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
254
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41) A vendor selling newspapers on a street corner is an example of a
A) single-channel, multiphase system.
B) single-channel, single-phase system.
C) multichannel, multiphase system.
D) multichannel, single-phase system.
Answer: B
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
42) Lines at banks where customers wait for a teller window are usually representative of a
A) single-channel, multiphase system.
B) single-channel, single-phase system.
C) multichannel, multiphase system.
D) multichannel, single-phase system.
Answer: D
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
43) Which of the following distributions is most often used to estimate the arrival pattern?
A) negative exponential
B) normal
C) Poisson
D) Erlang
Answer: C
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
255
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44) A single automatic car wash with one bay and a cycle time of 2.5 minutes is what type of model?
A) M/M/1
B) M/M/2
C) M/D/2
D) M/D/1
Answer: D
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
45) A single automatic car wash with one bay and a service time that is normally distributed is what type
of model?
A) M/M/1
B) M/D/2
C) M/D/1
D) M/G/1
Answer: D
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
46) A suburban specialty restaurant has developed a single drive-thru window. Customers order, pay,
and pick up their food at the same window. Arrivals follow a Poisson distribution, while service times
follow an exponential distribution. What type of queuing model is exhibited in this problem?
A) M/M/1
B) M/M/2
C) M/D/2
D) M/D/1
Answer: D
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Concept
256
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47) A professor holds office hours during final exam week and discovers much to his dismay that his
sudden popularity affords him little time to engage in his favorite activity, watching cat videos. Fifteen
students per hour arrive at his office and he patiently answers questions, averaging three minutes per
student. If the average cat video is 60 seconds, how many videos can the professor watch in an hour?
A) 15
B) 18
C) 20
D) 24
Answer: A
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
48) A professor holds office hours during final exam week and discovers much to his dismay that his
sudden popularity affords him little time to engage in his favorite activity, watching cat videos. Fifteen
students per hour arrive at his office and he patiently answers questions, averaging three minutes per
student. On average, how many students are waiting to ask questions?
A) 2.00
B) 2.25
C) 2.50
D) 2.75
Answer: B
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
257
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49) A professor holds office hours during final exam week and discovers much to his dismay that his
sudden popularity affords him little time to engage in his favorite activity, watching cat videos. Fifteen
students per hour arrive at his office and he patiently answers questions, averaging three minutes per
student. On average, how long must a student wait in line to get their last-minute questions answered?
A) 3 minutes
B) 6 minutes
C) 9 minutes
D) 12 minutes
Answer: C
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
50) A professor holds office hours during final exam week and discovers much to his dismay that his
sudden popularity affords him little time to engage in his favorite activity, watching cat videos. Fifteen
students per hour arrive at his office and he patiently answers questions, averaging three minutes per
student. A student joins the line at 9:45 am and the test is at 10:00 am the same morning. How much
time does the student have after getting his question answered to get to the exam room?
A) 12 minutes
B) 9 minutes
C) 6 minutes
D) 3 minutes
Answer: D
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
258
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51) Customers enter the waiting line at a cafeteria on a first-come, first-served basis. The arrival rate
follows a Poisson distribution, while service times follow an exponential distribution. If the average
number of arrivals is four per minute and the average service rate of a single server is seven per minute,
what is the average number of customers in the system?
A) 0.43
B) 1.67
C) 0.57
D) 1.33
Answer: D
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
52) Customers enter the waiting line at a cafeteria on a first-come, first-served basis. The arrival rate
follows a Poisson distribution, while service times follow an exponential distribution. If the average
number of arrivals is four per minute and the average service rate of a single server is seven per minute,
what is the average number of customers waiting in line behind the person being served?
A) 0.76
B) 0.19
C) 1.33
D) 1.67
Answer: A
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
259
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53) Customers enter the waiting line to pay for food as they leave a cafeteria on a first-come, first-served
basis. The arrival rate follows a Poisson distribution, while service times follow an exponential
distribution. If the average number of arrivals is four per minute and the average service rate of a single
server is seven per minute, what proportion of the time is the server busy?
A) 0.43
B) 0.57
C) 0.75
D) 0.25
Answer: B
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
54) Customers enter the waiting line to pay for food as they leave a cafeteria on a first-come, first-served
basis. The arrival rate follows a Poisson distribution, while service times follow an exponential
distribution. If the average number of arrivals is four per minute and the average service rate of a single
server is seven per minute, on average, how much time will elapse from the time a customer enters the
line until he/she leaves the cafeteria?
A) 0.67 minute
B) 0.50 minute
C) 0.75 minute
D) 0.33 minute
Answer: D
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
260
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55) At a local fast-food joint, cars arrive randomly at a rate of 12 every 30 minutes. The fast food joint
takes an average of 2 minutes to serve each arrival. The utilization factor for this system is
A) 0.467.
B) 0.547.
C) 0.800.
D) 0.133.
Answer: C
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
56) At a local fast food joint, cars arrive randomly at a rate of 12 every 30 minutes. Service times are
random (exponential) and average 2 minutes per arrival. The average time in the queue for each arrival
is
A) 2 minutes.
B) 4 minutes.
C) 6 minutes.
D) 8 minutes.
Answer: D
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
57) Which of the following distributions is most often used to estimate service times?
A) negative exponential
B) normal
C) Poisson
D) Erlang
Answer: A
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
261
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58) Most systems use a queue discipline known as
A) shortest processing time.
B) longest processing time.
C) FIFO.
D) earliest due date.
Answer: C
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
59) A queuing system with a normally distributed arrival pattern, exponential service times, and three
servers would be described as
A) G/G/3.
B) M/M/3.
C) G/M/3.
D) M/G/3.
Answer: C
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
60) The initial state of a queuing system (for example, when a restaurant first opens), is referred to as the
________ state.
A) steady
B) primary
C) introductory
D) transient
Answer: D
Diff: Moderate
Topic: SOME GENERAL OPERATING CHARACTERISTIC RELATIONSHIPS
LO: 12.7: Understand Little's Flow Equations.
AACSB: Analytical thinking
Classification: Concept
262
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61) A post office has a single line for customers waiting for the next available postal clerk. There are
two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson
distribution, while the service time follows an exponential distribution. What type of queuing model
applies here?
A) M/M/1
B) M/M/2
C) M/D/2
D) M/D/1
Answer: B
Diff: Easy
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
62) A post office has a single line for customers waiting for the next available postal clerk. There are
two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson
distribution, while the service time follows a normal distribution. What type of queuing model applies
here?
A) M/M/2
B) M/D/2
C) M/D/1
D) M/G/2
Answer: D
Diff: Easy
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
263
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63) A post office has a single line for customers waiting for the next available postal clerk. There are
two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson
distribution, while the service time follows an exponential distribution. The average arrival rate is three
per minute and the average service rate is two per minute for each of the two clerks. What is the average
length of the line?
A) 3.429
B) 1.929
C) 1.143
D) 0.643
Answer: B
Diff: Difficult
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
64) A post office has a single line for customers waiting for the next available postal clerk. There are
two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson
distribution, while the service time follows an exponential distribution. The average arrival rate is three
per minute and the average service rate is two per minute for each of the two clerks. How long does the
average person spend waiting for a clerk?
A) 3.429 minutes
B) 1.929 minutes
C) 1.143 minutes
D) 0.643 minute
Answer: D
Diff: Difficult
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
264
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65) A post office has a single line for customers waiting for the next available postal clerk. There are
two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson
distribution, while the service time follows an exponential distribution. The average arrival rate is three
per minute and the average service rate is two per minute for each of the two clerks. What proportion of
time are both clerks idle?
A) 0.643
B) 0.250
C) 0.750
D) 0.143
Answer: B
Diff: Difficult
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
Table 12-1
M/M/2
Mean Arrival Rate:
Mean Service Rate:
Number of Servers:
Server wage
Customer waiting cost
Probability of zero customers in system:
20 customers/hour
12 customers/hour
2
$10/hour
$20/hour
0.280
66) According to the information provided in Table 12-1, on average, how many customers are in the
line?
A) 3.79
B) 3.33
C) 4.25
D) 4.33
Answer: A
Diff: Moderate
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
265
Copyright © 2012 Pearson Education, Inc. publishing as Prentice Hall
67) According to the information provided in Table 12-1, how long does a customer wait on average?
A) 11 minutes
B) 11 minutes 30 seconds
C) 12 minutes 15 seconds
D) 12 minutes 45 seconds
Answer: B
Diff: Moderate
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
68) Using the information provided in Table 12-1, counting each person being served and the people in
line, on average, how many customers would be in this system?
A) 4.85
B) 5.05
C) 5.45
D) 6.15
Answer: C
Diff: Moderate
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
69) According to the information provided in Table 12-1, what is the hourly total cost of the system for
customers and servers? Assume that servers are paid only when they are helping customers.
A) $117.67
B) $121.47
C) $129.09
D) $125.76
Answer: D
Diff: Difficult
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
266
Copyright © 2012 Pearson Education, Inc. publishing as Prentice Hall
70) According to the information provided in Table 12-1, what percentage of the total available service
time is being used?
A) 83.0%
B) 87.0%
C) 78.3%
D) 60.0%
Answer: A
Diff: Moderate
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
71) According to the information provided in Table 12-1, what is the average amount of time a customer
waits and is served?
A) 15 minutes 40 seconds
B) 16 minutes 20 seconds
C) 17 minutes
D) 17 minutes 40 seconds
Answer: B
Diff: Moderate
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
267
Copyright © 2012 Pearson Education, Inc. publishing as Prentice Hall
Table 12-2
M/M/2
Mean Arrival Rate:
Mean Service Rate:
Number of Servers:
5 occurrences per minute
3 occurrences per minute
2
Queue Statistics:
Mean Number of Units in the System:
Mean Number of Units in the Queue:
Mean Time in the System:
Mean Time in the Queue:
Service Facility Utilization Factor:
Probability in No Units in System:
5.455
3.788
1.091 minutes
0.758 minutes
0.833
0.091
72) According to the information provided in Table 12-2, which presents a queuing problem solution, on
average, how many units are in the line?
A) 5.455
B) 3.788
C) 1.091
D) 0.758
E) 0.833
Answer: B
Diff: Easy
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
73) According to the information provided in Table 12-2, which presents a queuing problem solution,
what proportion of time is at least one server busy?
A) 0.833
B) 0.758
C) 0.091
D) 0.909
Answer: D
Diff: Easy
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
268
Copyright © 2012 Pearson Education, Inc. publishing as Prentice Hall
Classification: Application
269
Copyright © 2012 Pearson Education, Inc. publishing as Prentice Hall
74) According to the information provided in Table 12-2, which presents a queuing problem solution,
there are two servers in this system. Counting each person being served and the people in line, on
average, how many people would be in this system?
A) 5.455
B) 3.788
C) 9.243
D) 10.900
Answer: A
Diff: Easy
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
Table 12-3
M/M/3
Mean Arrival Rate:
Mean Service Rate:
Number of Servers:
4 occurrences per minute
2 occurrences per minute
3
Queue Statistics:
Mean Number of Units in the System:
Mean Number of Units in the Queue:
Mean Time in the System:
Mean Time in the Queue:
Service Facility Utilization Factor:
Probability in No Units in System:
2.889
0.889
0.722 minutes
0.222 minutes
0.667
0.111
75) According to the information provided in Table 12-3, which presents a queuing problem solution,
what proportion of time is the system totally empty?
A) 0.111
B) 0.333
C) 0.889
D) 0.667
Answer: A
Diff: Easy
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
270
Copyright © 2012 Pearson Education, Inc. publishing as Prentice Hall
Classification: Application
271
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76) According to the information provided in Table 12-3, which presents a queuing problem solution, on
average, how long does each customer spend waiting in line?
A) 0.333 minute
B) 0.889 minute
C) 0.222 minute
D) 0.722 minute
Answer: C
Diff: Easy
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
77) According to the information provided in Table 12-3, which presents a queuing problem solution,
what is the utilization rate of the service facility?
A) 0.889
B) 0.222
C) 0.722
D) 0.667
Answer: D
Diff: Easy
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
78) If everything else remains constant, including the mean arrival rate and service rate, except that the
service time becomes constant instead of exponential
A) the average queue length will be halved.
B) the average waiting time will be doubled.
C) the average queue length will be doubled.
D) There is not enough information to know what will happen to the queue length and waiting time.
Answer: A
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
272
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79) At an automatic car wash, cars arrive randomly at a rate of 7 cars every 30 minutes. The car wash
takes exactly 4 minutes (this is constant). On average, what would be the length of the line?
A) 8.171
B) 7.467
C) 6.53
D) 0.467
Answer: C
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
80) At an automatic car wash, cars arrive randomly at a rate of 7 every 30 minutes. The car wash takes
exactly 4 minutes (this is constant). On average, how long would each car spend at the car wash?
A) 28 minutes
B) 32 minutes
C) 17 minutes
D) 24 minutes
Answer: B
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
81) At an automatic car wash, cars arrive randomly at a rate of 7 every 30 minutes. The car wash takes
exactly 4 minutes (this is constant). On average, how long would each driver have to wait before
receiving service?
A) 28 minutes
B) 32 minutes
C) 17 minutes
D) 24 minutes
Answer: A
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
273
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82) At an automatic car wash, cars arrive randomly at a rate of 7 every 30 minutes. The car wash takes
exactly 4 minutes (this is constant). On average, how many customers would be at the car wash (waiting
in line or being serviced)?
A) 8.17
B) 7.46
C) 6.53
D) 0.46
Answer: B
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
83) At a local fast food joint, cars arrive randomly at a rate of 12 every 30 minutes. The fast food joint
takes exactly 2 minutes (this is constant). The average total time in the system is
A) 5.4 minutes.
B) 6.0 minutes.
C) 8.0 minutes.
D) 2.5 minutes.
Answer: B
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
274
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Table 12-4
The sentient car wash in Luther knows she is in for a busy day when dawn breaks on a gorgeous spring
morning. She is capable of washing a car every four minutes, and by the looks of things, it is reasonable
to expect a steady stream of twelve cars per hour arriving. Because she is fully automatic, she knows
that the four-minute estimate is accurate and invariant. She values her time at $10 per hour. Yes, it
seems low, but as a single bay car wash, there are few other jobs in town she is qualified for. (We won't
get into her unsuccessful turn at the beauty salon.) She estimates that customer time can be valued at $15
per hour.
84) According to the information provided in Table 12-4, how much time will the average customer
spend waiting in line?
A) 8 minutes
B) 9 minutes
C) 10 minute
D) 11 minute
Answer: A
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
85) According to the information provided in Table 12-4, on average, how many customers are in line?
A) 1.2 cars
B) 1.6 cars
C) 1.75 cars
D) 2.1 cars
Answer: B
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
275
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86) According to the information provided in Table 12-4, how many minutes per hour will the car wash
be idle and able to ponder the meaning of life?
A) 9 minutes
B) 10 minutes
C) 12 minutes
D) 15 minutes
Answer: C
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
87) According to Table 12-4, what is the total hourly cost of the system for customers and the car wash
herself? Assume the car wash is paid only when she is washing cars.
A) $38
B) $40
C) $42
D) $44
Answer: D
Diff: Difficult
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
88) According to Table 12-4, what is the total number of cars in the system?
A) 2.40
B) 2.75
C) 3.10
D) 3.45
Answer: A
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
276
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Table 12-5
M/D/1
Mean Arrival Rate:
Constant Service Rate:
5 occurrences per minute
7 occurrences per minute
Queue Statistics:
Mean Number of Units in the System:
Mean Number of Units in the Queue:
Mean Time in the System:
Mean Time in the Queue:
Service Facility Utilization Factor:
1.607
0.893
0.321 minutes
0.179 minutes
0.714
89) According to the information provided in Table 12-5, which presents the solution for a queuing
problem with a constant service rate, on average, how much time is spent waiting in line?
A) 1.607 minutes
B) 0.714 minute
C) 0.179 minute
D) 0.893 minute
Answer: C
Diff: Easy
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
90) According to the information provided in Table 12-5, which presents the solution for a queuing
problem with a constant service rate, on average, how many customers are in the system?
A) 0.893
B) 0.714
C) 1.607
D) 0.375
Answer: C
Diff: Easy
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
277
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91) According to the information provided in Table 12-5, which presents a queuing problem solution for
a queuing problem with a constant service rate, on average, how many customers arrive per time period?
A) 5
B) 7
C) 1.607
D) 0.893
Answer: A
Diff: Easy
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
92) According to the information provided in Table 12-5, which presents the solution for a queuing
problem with a constant service rate, on average, how many minutes does a customer spend in the
system?
A) 0.893 minute
B) 0.321 minute
C) 0.714 minute
D) 1.607 minutes
Answer: B
Diff: Easy
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
93) According to the information provided in Table 12-5, which presents the solution for a queuing
problem with a constant service rate, the probability that the server is idle is
A) 0.217.
B) 0.643.
C) 0.286.
D) 0.714.
Answer: C
Diff: Easy
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
278
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94) Thanks to a generous and eccentric donor, the school of business has 3 fax machines. The toner in
each machine needs to be changed after about 5 hours of use. There is one unit secretary who is
responsible for the fax machine maintenance. It takes him 15 minutes to replace the toner cartridge.
What is the probability that none of the fax machines need toner?
A) 1.1500
B) 1.1658
C) .8578
D) .7696
Answer: C
Diff: Difficult
Topic: FINITE POPULATION MODEL (M/M/1 WITH FINITE SOURCE)
LO: 12.6: Analyze a variety of operating characteristics of waiting lines for single channel model with
exponential service times and finite calling populations.
AACSB: Analytical thinking
Classification: Application
95) Thanks to a generous and eccentric donor, the school of business has 3 fax machines. The toner in
each machine needs to be changed after about 5 hours of use. There is one unit secretary who is
responsible for the fax machine maintenance. It takes him 15 minutes to replace the toner cartridge.
What is the average number of fax machines in the queue?
A) 0.5658 fax machines
B) 0.3304 fax machines
C) .0563 fax machine
D) .0142 fax machine
Answer: D
Diff: Difficult
Topic: FINITE POPULATION MODEL (M/M/1 WITH FINITE SOURCE)
LO: 12.6: Analyze a variety of operating characteristics of waiting lines for single channel model with
exponential service times and finite calling populations.
AACSB: Analytical thinking
Classification: Application
96) Thanks to a generous and eccentric donor, the school of business has 3 fax machines. The toner in
each machine needs to be changed after about 5 hours of use. There is one unit secretary who is
responsible for the fax machine maintenance. It takes him 15 minutes to replace the toner cartridge.
What is the average number of fax machines in the system?
A) .0142 fax machine
B) .1563 fax machine
C) .0249 fax machine
D) .2749 fax machine
Answer: B
Diff: Difficult
Topic: FINITE POPULATION MODEL (M/M/1 WITH FINITE SOURCE)
LO: 12.6: Analyze a variety of operating characteristics of waiting lines for single channel model with
279
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exponential service times and finite calling populations.
AACSB: Analytical thinking
Classification: Application
97) Thanks to a generous and eccentric donor, the school of business has 3 fax machines. The toner in
each machine needs to be changed after about 5 hours of use. There is one unit secretary who is
responsible for the fax machine maintenance. It takes him 15 minutes to replace the toner cartridge.
What is the average waiting time in the queue?
A) .0142 hour
B) .1563 hour
C) .0249 hour
D) .2749 hour
Answer: C
Diff: Difficult
Topic: FINITE POPULATION MODEL (M/M/1 WITH FINITE SOURCE)
LO: 12.6: Analyze a variety of operating characteristics of waiting lines for single channel model with
exponential service times and finite calling populations.
AACSB: Analytical thinking
Classification: Application
98) Thanks to a generous and eccentric donor, the school of business has 3 fax machines. The toner in
each machine needs to be changed after about 5 hours of use. There is one unit secretary who is
responsible for the fax machine maintenance. It takes him 15 minutes to replace the toner cartridge.
What is the probability that one of the fax machines needs toner?
A) 0.22
B) 0.19
C) 0.16
D) 0.13
Answer: D
Diff: Difficult
Topic: FINITE POPULATION MODEL (M/M/1 WITH FINITE SOURCE)
LO: 12.6: Analyze a variety of operating characteristics of waiting lines for single channel model with
exponential service times and finite calling populations.
AACSB: Analytical thinking
Classification: Application
280
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Table 12-6
Customers arrive at coffee shop at a rate of 40 per hour. There are 2 servers available and it takes an
average of 1 minute to serve each customer.
99) Using Table 12-6, what proportion of time are the servers busy?
A) 0
B) 0.333
C) 0.5
D) 0.6667
Answer: B
Diff: Moderate
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
100) Using Table 12-6, what is the probability of no customers in the system?
A) 0
B) 0.333
C) 0.5
D) 0.667
Answer: C
Diff: Moderate
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
101) Using Table 12-6, what is the average number of customers in the coffee shop?
A) 0.0833
B) 0.5
C) 0.75
D) 1.33
Answer: C
Diff: Moderate
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
281
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AACSB: Analytical thinking
Classification: Application
102) Using Table 12-6, what is the average number of customers waiting in line?
A) 0.0833
B) 0.5
C) 0.75
D) 1.33
Answer: A
Diff: Moderate
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
103) The school of business has 3 fax machines. The toner in each machine needs to be changed after
about 5 hours of use. There is one unit secretary who is responsible for the fax machine maintenance. It
takes him 15 minutes to replace the toner cartridge. What is the average time spent in the system?
A) .0142 hour
B) .1563 hour
C) .0249 hour
D) .2749 hour
Answer: D
Diff: Difficult
Topic: FINITE POPULATION MODEL (M/M/1 WITH FINITE SOURCE)
LO: 12.6: Analyze a variety of operating characteristics of waiting lines for single channel model with
exponential service times and finite calling populations.
AACSB: Analytical thinking
Classification: Application
104) The school of business has 3 fax machines. The toner in each machine needs to be changed after
about 5 hours of use. There is one unit secretary who is responsible for the fax machine maintenance. It
takes him 15 minutes to replace the toner cartridge. What is the probability that 2 fax machines need
toner at the same time?
A) .8576
B) .1286
C) .0129
D) .1415
Answer: C
Diff: Difficult
Topic: FINITE POPULATION MODEL (M/M/1 WITH FINITE SOURCE)
LO: 12.6: Analyze a variety of operating characteristics of waiting lines for single channel model with
282
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exponential service times and finite calling populations.
AACSB: Analytical thinking
Classification: Application
283
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105) A new shopping mall is considering setting up an information desk manned by one employee.
Based upon information obtained from similar information desks, it is believed that people will arrive at
the desk at the rate of 15 per hour. It takes an average of two minutes to answer a question. It is assumed
that arrivals are Poisson and answer times are exponentially distributed.
(a) Find the probability that the employee is idle.
(b) Find the proportion of time that the employee is busy.
(c) Find the average number of people receiving and waiting to receive information.
(d) Find the average number of people waiting in line to get information.
(e) Find the average time a person seeking information spends at the desk.
(f) Find the expected time a person spends waiting in line to have his question answered.
Answer:
(a) Po = 0.50
(b) ρ = 0.50
(c) L = 1
(d) Lq = 0.50
(e) W = 0.0667 hour
(f) Wq = 0.0333 hour
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
284
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106) A new shopping mall is considering setting up an information desk manned by one employee.
Based upon information obtained from similar information desks, it is believed that people will arrive at
the desk at the rate of 15 per hour. It takes exactly two minutes to answer each question. It is assumed
that arrivals are Poisson.
(a) Find the probability that the employee is idle.
(b) Find the proportion of time that the employee is busy.
(c) Find the average number of people receiving and waiting to receive information.
(d) Find the average number of people waiting in line to get information.
(e) Find the average time a person seeking information spends at the desk.
(f) Find the expected time a person spends waiting in line to have his question answered.
Answer:
(a) Po = 0.50
(b) ρ = 0.50
(c) L = 0.75
(d) Lq = 0.25
(e) W = 0.05 hour
(f) Wq = 0.03 hour
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
285
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107) Sam the Vet is running a rabies vaccination clinic for dogs at the local grade school. Sam can
vaccinate a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly
throughout the day at a rate of 1 dog every 6 minutes, according to a Poisson distribution. Also assume
that Sam's vaccinating times are exponentially distributed.
(a) Find the probability that Sam is idle.
(b) Find the proportion of time that Sam is busy.
(c) Find the average number of dogs receiving or waiting to be vaccinated.
(d) Find the average number of dogs waiting to be vaccinated.
(e) Find the average time a dog waits before getting vaccinated.
(f) Find the average amount (mean) of time a dog spends between waiting in line and getting vaccinated.
Answer:
(a) Po = 0.5
(b) ρ = 0.5
(c) L = 1
(d) Lq = 0.5
(e) Wq = 0.05 hour
(f) W = 0.1 hour
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
286
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108) Sam the Vet is running a rabies vaccination clinic for dogs at the local grade school. Sam can
vaccinate a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly
throughout the day at a rate of 1 dog every 4 minutes, according to a Poisson distribution. Also assume
that Sam's vaccinating times are exponentially distributed.
(a) Find the probability that Sam is idle.
(b) Find the proportion of time that Sam is busy.
(c) Find the average number of dogs receiving or waiting to be vaccinated.
(d) Find the average number of dogs waiting to be vaccinated.
(e) Find the average time a dog waits before getting vaccinated.
(f) Find the average amount (mean) of time a dog spends between waiting in line and getting vaccinated.
Answer: a. Po = 0.25
b. ρ = 0.75
c. L = 3
d. Lq = 2.25
e. Wq = 0.15 hour
f. W = 0.2 hour
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
109) A dry cleaner has a single drive-thru window for customers. The arrival rate of cars follows a
Poisson distribution, while the service time follows an exponential distribution. The average arrival rate
is 16 per hour and the average service time is three minutes.
(a) What is the average number of cars in the line?
(b) What is the average time spent waiting to get to the service window?
(c) What percentage of time is the dry cleaner's drive-thru window idle?
(d) What is the probability there are more than 2 cars at the drive-thru window?
Answer:
(a) Lq = 3.2
(b) Wq = 0.2 hour (12 minutes)
(c) Po = 0.20
(d) Pn > k = 0.512
Diff: Moderate
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
287
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110) A dry cleaner has a single drive-thru window for customers. The arrival rate of cars follows a
Poisson distribution, while the service time follows an exponential distribution. The average arrival rate
is 16 per hour and the average service time is three minutes. If the dry cleaner wants to accommodate
(have enough room for) all of the waiting cars at least 96 percent of the time, how many car-lengths
should they make the driveway leading to the window?
Answer: The probability of having more than 14 cars in the system is (16/20)14 + 1 = 0.035, so they
should make the driveway approximately 13 car-lengths long (because one car will be at the service
window). (The probability of having more than 13 cars in the system is 0.044 (which is too high), and
the percentage only gets worse as the queue length is shortened.)
Diff: Difficult
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
111) Sam the Vet is running a rabies vaccination clinic for dogs at the local grade school. Sam can
vaccinate a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly
throughout the day at a rate of 1 dog every 6 minutes, according to a Poisson distribution. Also assume
that Sam's vaccinating times are exponentially distributed. Sam would like to have each waiting dog
placed in a holding pen. If Sam wants to be certain he has enough cages to accommodate all dogs at
least 90 percent of the time, how many cages should he prepare?
Answer: He needs to prepare 2 cages. The probability of having more than 3 dogs in the system is
0.0625 while the probability of having more than 2 dogs in the system is 0.125.
Diff: Difficult
Topic: SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND
EXPONENTIAL SERVICE TIMES (M/M/1)
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
288
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112) A new shopping mall is considering setting up an information desk operated by two employees.
Based on information obtained from similar information desks, it is believed that people will arrive at
the desk at the rate of 20 per hour. It takes an average of 4 minutes to answer a question. It is assumed
that arrivals are Poisson and answer times are exponentially distributed.
(a) Find the proportion of the time that the employees are busy.
(b) Find the average number of people waiting in line to get some information.
(c) Find the expected time a person spends just waiting in line to have his question answered.
Answer:
(a) ρ = 0.667
(b) Lq = 1.0667
(c) Wq = 0.0533 hour
Diff: Difficult
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
113) Cars arrive at a parking lot entrance at the rate of 20 per hour. The average time to get a ticket and
proceed to a parking space is two minutes. There are two lot attendants at the current time. The Poisson
and exponential distribution appear to be relevant in this situation.
(a) What is the probability that an approaching auto must wait?
(b) What is the average waiting time?
(c) What is the average number of autos waiting to enter the garage?
Answer:
(a) Po = 0.50
(b) Wq = 0.25 minute
(c) Lq = 0.0833 auto
Diff: Difficult
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
289
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114) Bank Boston has a branch at Bryant College. The branch is busiest at the beginning of the college
year when freshmen and transfer students open accounts. This year, freshmen arrived at the office at a
rate of 40 per day (8-hour day). On average, it takes the Bank Boston staff person about ten minutes to
process each account application. The bank is considering having one or two tellers. Each teller is paid
$12 per hour and the cost of waiting in line is assumed to be $8 per hour.
(a) What is the total daily waiting cost for the single teller model?
(b) What is the total daily waiting cost for the two-teller model?
(c) What is the total daily service cost for the single teller model?
(d) What is the total daily service cost for the two-teller model?
(e) Which model is preferred?
Answer:
(a) Total wait cost = [(5 * .833 hours) (8)] * 8 hours/day = $266.56
(b) Total wait cost = [(5 * .035 hours) (8)] * 8 hours/day = $11.20
(c) Total service cost = (1 * $12) * 8 hours/day = $96
(d) Total service cost = (2 * $12) * 8 hours/day = $192
(e) Two channel model
Diff: Difficult
Topic: VARIOUS
LO: 12.3: Analyze a variety of operating characteristics of waiting lines for single channel models with
exponential service times and infinite calling populations. 12.4: Analyze a variety of operating
characteristics of waiting lines for multi-channel models with exponential service times and infinite
calling populations.
AACSB: Analytical thinking
Classification: Application
290
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115) At the start of football season, the ticket office gets busy the day before the first game. Customers
arrive at the rate of four every ten minutes. A ticket seller can service a customer in four minutes.
Traditionally, there are two ticket sellers working. The university is considering an automated ticket
machine similar to the airlines' e-ticket system. The automated ticket machine can service a customer in
2 minutes.
(a) What is the average length of the queue for the in-person model?
(b) What is the average length of the queue for the automated system model?
(c) What is the average time in the system for the in-person model?
(d) What is the average time in the system for the automated system model?
(e) Assume the ticket sellers earn $8 per hour and the machine costs $20 per hour (amortized over 5
years). The wait time is only $4 per hour because students are patient. What is the total cost of each
model?
Answer:
(a) Lq = 2.844
(b) Lq = 1.6
(c) W = 0.1852 hour or 11.11 minutes
(d) W = 0.1 hour or 6 minutes
(e) Total cost (in-person) = (2 ∗ $8/hour) + (24/hour ∗ .1852 hours) ($4/hour) = $33.78
Total cost (automated) = (1 ∗ $20/hour) + (24/hour ∗ .1 hour) ($4/hour) = $29.60
Diff: Difficult
Topic: VARIOUS
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations. 12.5 Analyze a variety of operating
characteristics of waiting lines for single channel models with deterministic service times and infinite
calling populations.
AACSB: Analytical thinking
Classification: Application
116) Consider a single-server queuing system with Poisson arrivals of 10 units per hour and a constant
service time of 2 minutes per unit. How long will the customer waiting time be in seconds, on average?
Answer: 10 / [(2)(30)(30 − 10)] = .00833333 hours = 0.5 minute = 30 seconds
Diff: Moderate
Topic: CONSTANT SERVICE TIME MODEL (M/D/1)
LO: 12.5 Analyze a variety of operating characteristics of waiting lines for single channel models with
deterministic service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
291
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117) There is a tutoring lab at a university that holds 20 students. Due to the popularity of the 3 tutors,
the lab is always at capacity. Each student approaches a tutor an average of 2 times per hour, and a tutor
spends on average 5 minutes per question from a student. The service time follows an exponential
distribution.
(a) What proportion of the time are the tutors busy?
(b) What is the average waiting time for students in queue?
Answer:
(a) ρ = 0.86
(b) Wq = 0.06 hour
Diff: Moderate
Topic: FINITE POPULATION MODEL (M/M/1 WITH FINITE SOURCE)
LO: 12.6: Analyze a variety of operating characteristics of waiting lines for single channel model with
exponential service times and finite calling populations.
AACSB: Analytical thinking
Classification: Application
118) A professor decides to hold a three-hour window open for student advising. The professor has 15
advisees. He's unsure if each advisee will show up, and it's possible that a single advisee could show up
multiple times during the 3-hour window. On average, the professor will spend 12 minutes with each
student. He usually expects each student to arrive once during the 3-hour window.
(a) What proportion of the time can the professor expect to be busy during the window?
(b) What is the expected number of students in queue during the window?
(c) What is the expected wait time in queue during the window?
Answer:
(a) ρ = 0.82
(b) Lq = 1.88
(c) Wq = 0.46 hour
Diff: Difficult
Topic: FINITE POPULATION MODEL (M/M/1 WITH FINITE SOURCE)
LO: 12.6: Analyze a variety of operating characteristics of waiting lines for single channel model with
exponential service times and finite calling populations.
AACSB: Analytical thinking
Classification: Application
292
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119) Customers arrive at a bank at a rate of one every minute. The bank has 3 tellers and on average, it
takes two minutes to service a customer.
(a) What proportion of time are the tellers busy?
(b) What is the average number of customers in the bank?
(c) What is the average weight time?
Answer:
(a) ρ = 0.67
(b) L = 2.89
(c) Wq = 0.01 hour = 0.89 minutes = 53.33 seconds
Diff: Difficult
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
120) Customers arrive at their friendly DMV at a rate of 45 people per hour. There are four servers that
can process customers at an average of 3 minutes.
(a) What is the average wait time?
(b) What is the average number of customers waiting?
(c) What is the average number of customers in the DMV?
Answer:
(a) Wq = 0.01 hours = .41 minutes = 24.81 seconds
(b) Lq = 0.31 customers
(c) L = 2.56
Diff: Difficult
Topic: MULTICHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL
SERVICE TIMES (M/M/m)
LO: 12.4: Analyze a variety of operating characteristics of waiting lines for multi-channel models with
exponential service times and infinite calling populations.
AACSB: Analytical thinking
Classification: Application
121) What is meant by a single-channel queuing system?
Answer: one service facility system fed by one queue
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
293
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122) What is meant by a multichannel queuing system?
Answer: more than one service facility all fed by the same queue
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
123) What is meant by a single-phase system?
Answer: Arrivals leave the system after receiving service at only one station.
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
124) What is meant by a multiphase system?
Answer: Service is provided at more than one station, one after the other.
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
125) What is the difference between customers balking and customers reneging? If you managed a retail
store how would you track and differentiate between customers that balked and reneged?
Answer: Balking occurs when customers decline to join the queue, typically because they see the line is
too long and they don't have enough time. Reneging occurs when customers join the queue and change
their mind later and depart the queue. Answers will vary as to how they can be tracked. It may be easier
to track those that renege if some part of the service process has already begun and customer
information is recorded. Alternatively, security camera footage could be checked at the end of each day
to see the number that joined a line and then left. Balking would probably be tougher to capture in most
situations.
Diff: Moderate
Topic: CHARACTERISTICS OF A QUEUING SYSTEM
LO: 12.2: Describe the basic queuing system configurations and the three parts of a queuing system: the
calling population, the queue itself, and the service facility.
AACSB: Analytical thinking
Classification: Concept
294
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126) What is the difference between a transient state and a steady state? How could you as a manager
distinguish between the two?
Answer: A steady state is the normal operating condition of the queuing system. A queuing system is in
a transient state before the steady state is reached. A manager would expect to be in a transient state at
opening time each day or after a holiday and be in steady state during most operating hours if most
queuing analysis assumptions are reasonable. For pure customer service situations, there may be
additional transient periods of the day, for example, a lunch or dinner rush at a restaurant.
Diff: Moderate
Topic: SOME GENERAL OPERATING CHARACTERISTIC RELATIONSHIPS
LO: 12.7: Understand Little's Flow Equations.
AACSB: Analytical thinking
Classification: Concept
127) Four thousand students are admitted each year at a large regional university. The average time to
complete a degree is six years and the university's retention rate initiative achieves 100% (no students
drop out or transfer). What is the student population?
Answer: 24,000 students; L = λW = 4000 students/year × 6 years
Diff: Easy
Topic: SOME GENERAL OPERATING CHARACTERISTIC RELATIONSHIPS
LO: 12.7: Understand Little's Flow Equations.
AACSB: Analytical thinking
295
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