Tom foresees fixed monthly expenses

ANSWER: FALSE
3.3 The decision maker has little or no control over a state of nature.

ANSWER: TRUE
3.4 Decision making under risk is a probabilistic decision situation.

ANSWER: TRUE
3.9 The maximax decision criterion is used by pessimistic decision makers and maximizes the maximum outcome for every alternative.

ANSWER: FALSE
3.10The maximin decision criterion is used by pessimistic decision makers and minimizes the maximum outcome for every alternative.

ANSWER: TRUE
3.12The decision theory processes of maximizing Expected Monetary Value and minimizing Expected Opportunity Loss should lead us to choose the same alternatives.

ANSWER: TRUE
3.13The several criteria (maximax, maximin, equally likely, criterion of realism, minimax) used for decision making under uncertainty may lead to the choice of different alternatives.

ANSWER: FALSE
3.18The expected value of sample information (EVSI) is equal to the expected value of the best decision with sample information (at no cost to gather) less the maximum expected monetary value (EMV).

ANSWER: TRUE
3.19The EMV approach and Utility theory always result in the same choice of alternatives.

3.21In 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
3.22A 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
3.27 Rational people make decisions that maximize the expected utility.

ANSWER: TRUE
3.28 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
3.29 The assignment of a utility value of 1 to an alternative implies that alternative is preferred to all others.

3.31The following figure illustrates a utility curve for someone who is a risk seeker.

(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.

(a) maximax.

(b) equally likely.

(a) It is the amount you would pay for any sample study.

(b) It is calculated as EMV minus EOL.

3.35If product demand follows a normal distribution and we want to apply marginal analysis, we need to know

(a) the mean sales estimate.

3.36The 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) none of the above

What decision would a pessimist make?

(a) Alternative 1
(b) Alternative 2
(c) Alternative 3
(d) Do Nothing
(e) none of the above

What decision should be made based on the minimax regret criterion?

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) none of the above

ANSWER: b

3.41The 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?

3.42 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?

(e) none of the above

ANSWER: c

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

(e) none of the above

ANSWER: a

How much should be paid for a perfect forecast of the state of nature?

ANSWER: c

46

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

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?

3.48 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.

(a) 0.20
(b) 0.30
(c) 0.40
(d) 0.10
(e) 0.90

ANSWER: e

ANSWER: b

3.51 Joel Turner sells donuts at the student service building. Daily sales of donuts are approximately normally distributed with a mean of 500 and a standard deviation of 40. Joel’s cost of purchasing each donut is 15 cents, and they are sold for 35 cents each. Joel plans to use a marginal analysis based on the normal distribution to make a decision. How many donuts should Joel purchase each day?

ANSWER: b

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3.54 Daily sales for submarine sandwiches are known to be 28, 29, 30, or 31 sandwiches with probabilities of 0.2, 0.3, 0.4, and 0.1, respectively. Sandwiches not sold during the day are worthless, and sandwiches can only be produced in the morning before the store opens. The cost of producing one sandwich is $2, while the selling price is $3.50. If you choose to produce 29 sandwiches in the morning to sell, what is the probability that you will have sandwiches left over when the store closes?

(a) 0.20
(b) 0.30
(c) 0.40
(d) 0.50
(e) 0.90

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3.57 Mickey sells newspapers on a corner every day. He pays 10 cents for each paper and sells them for 25 cents. He knows that the demand is always for 30, 40, or 50 papers, but he doesn't know ahead of time which of these will occur. Papers left at the end of the day are sold to a paper company. If he decides to purchase 40 papers but demand is only for 30, at what price must he sell the remaining papers to the paper company to earn a profit of $3.70?

(a) $0.05
(b) $0.04
(c) $0.03
(d) $0.02
(e) none of the above

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Decision Analysis ● Chapter 3

(a) $40/hr
(b) $50/hr
(c) $60/hr
(d) $70/hr
(e) none of the above

ANSWER: b

(d) a sequence of decisions must be made.

(e) all possible outcomes and alternatives are not known.

(e) none of the above

ANSWER: a

ANSWER: a

3.64 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?

(b) knowing, ahead of time, the actual outcome of the decision. (c) additional information.

(d) measurements of utility.

Decision Analysis ● Chapter 3

3.67 The following table provides information regarding probabilities for survey results for two states of nature.

The prior probability of a favorable market is 0.70, and an unfavorable market 0.30.

Determine the probability that the survey will predict a favorable market.

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Decision Analysis ● Chapter 3

(d) posterior probabilities.

(e) expected monetary values (EMV).

(c) increases as the monetary value increases.

(d) increases at a decreasing rate as monetary value increases.

(b) utility assessment.
(c) a risk seeker.

(d) conditional values.
(e) expected utilities.

(d) inflation plays a critical part in the evaluation.

(e) none of the above

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Decision Analysis ● Chapter 3

(d) A rational decision maker could not possibly choose alternative 2.

(e) none of the above

(c) Mr. Weed is not rational.

(d) (a) or (c)
(e) none of the above

ANSWER: e

3.77 It is sometimes said that "Those who gamble the most are the ones who can least afford to lose." These people gamble because

(e) none of the above

ANSWER: d

3.79 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)

(b) minimum EOL = $1,600

ANSWERS:

(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

Decision Analysis ● Chapter 3

3.82 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.

(b)

(c) They should build the new line.

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?

3.84 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:

$670,000*X = $560,000

X = $560,000/$670,000 = 0.836

ANSWER:

If we define X = probability of High Demand, then:

Decision Analysis ● Chapter 3

3.86 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 they can sell any leftover goods to a discount store, but they are uncertain as to the price the discount store will pay. For what price to be paid by the discount store would they order 70 cases of dresses in February?

(1300 + 10X) *0.4 + 1800*0.5 + 1800*0.1 =
(1100+20X)*0.4 + (1600+10X)*0.5 + 2100*0.1

520+ 4X + 900 +180 = 440 + 8X +800 + 5X +210

Decision Analysis ● Chapter 3

3.87 Norman L. Flowers holds the exclusive university contract for donut sales. The demand (based on historical records) appears to follow the following distribution:

3.89 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:

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Decision Analysis ● Chapter 3

(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.

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Decision Analysis ● Chapter 3

(a) 0.82
(b) 0.11

3.93 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 0.8 probability that the survey will be favorable given a successful store. There is also a 0.7 probability that the survey will be unfavorable given an unsuccessful store. What is the probability that the survey will be unfavorable?

ANSWER:

(a) 0.18
(b) 0.89

Using expected utility theory, what should Mark do?

ANSWER:

U(50000) = ? U(-10000) = 0.22
U(80000) = 1 U(-30000) = 0

For what value of utility for $50,000, U(50000), will Mark be indifferent between the two alternatives?

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Decision Analysis ● Chapter 3

ANSWER: decision making with certain knowledge of the consequence of every outcome

3.99 Briefly describe decision making under risk.

ANSWER: a node from which one of several alternatives may be chosen

3.102In general terms, describe a state of nature node.

ANSWER: EVSI = EV (best decision with sample information) – EV (of best decision without sample information)

3.105Describe the utility curve of a risk seeker.

ANSWER: utility increasing at a decreasing rate as the monetary value increases 3.107Describe utility assessment.

ANSWER: Assign the worst outcome a utility of 0 and the best outcome a utility of 1.