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
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
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
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
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
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
76) The Hurwicz criterion coefficient of realism measures the decision maker’s degree of ________.
A) utility
B) pessimism
C) certainty
D) optimism
E) regret
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
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).
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
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.
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
82) Utility values typically range from
A) –1 to 1
B) 1 to 10
C) 0 to 1
D) 1 to 100
E) None of the above
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
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
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
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
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?
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?
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).
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)
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).
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.
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.
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?
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.
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?
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?
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?
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?
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?
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?
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?
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?
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?
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?
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?
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?
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?
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?
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?
110) Briefly describe decision making under certainty.
111) Briefly describe decision making under risk.
112) Briefly describe decision making under uncertainty.
113) List the six steps in decision making.
114) Describe the structure of a payoff table.
115) Briefly describe decision tree analysis.
116) Briefly describe EVSI.
117) Describe the utility curve of a risk seeker.
118) Describe the utility curve of a risk avoider.
119) List the five major decision criteria used when making decisions under uncertainty.