CH 13 - Decision Analysis. Questions and Answers

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True / False 1. Sample information with an efficiency rating of 100% is perfect information. a. True b. False 2. States of nature should be defined so that one and only one will actu... ally occur. a. True b. False 3. Decision alternatives are structured so that several could occur simultaneously. a. True b. False 4. Square nodes in a decision tree indicate that a decision must be made. a. True b. False 5. Circular nodes in a decision tree are considered chance nodes. a. True b. False 6. Risk analysis helps the decision maker recognize the difference between the expected value of a decision alternative and the payoff that may actually occur. a. True b. False 7. The expected value of an alternative can never be negative. a. True b. False 8. For a chance node, the expected value is the weighted average of the payoffs, where the weights are the state-of-nature probabilities. a. True b. False 9. EVPI is always greater than or equal to EVSI. a. True b. False 10. After all probabilities and payoffs are placed on a decision tree, the decision maker calculates expected values at state-of-nature nodes and makes selections at decision nodes. a. True b. False 11. A decision strategy is a sequence of decisions and chance outcomes where the decisions chosen depend on the yet-to-be-determined outcomes of chance events. a. True b. False 12. Under the minimax regret approach to decision making, EVPI equals the expected regret that is associated with the minimax decision. a. True b. False 13. The expected value approach is more appropriate for a one-time decision than a repetitive decision. a. True b. False 14. Maximizing the expected payoff and minimizing the expected opportunity loss result in the same recommended decision. a. True b. False 15. The expected value of sample information can never be less than the expected value of perfect information. a. True b. False 16. Regret is the difference between the payoff associated with a particular decision alternative and the payoff associated with the decision that would yield the most desirable payoff for a given state of nature. a. True b. False 17. The primary value of decision trees is that they provide a useful way to organize how operations managers think about complex multiphase decisions. a. True b. False 18. A high efficiency rating indicates that the sample information is almost as good as perfect information. a. True b. False 19. When the expected value approach is used to select a decision alternative, the payoff that actually occurs will usually have a value different from the expected value. a. True b. False 20. The decision alternative with the best expected monetary value will always be the most desirable decision. a. True b. False 21. When monetary value is not the sole measure of the true worth of the outcome to the decision maker, monetary value should be replaced by utility. a. True b. False 22. Utility is the term for a measure of the total worth or relative desirability of a particular outcome. a. True b. False 23. As long as the monetary value of payoffs stays within a range that the decision maker considers reasonable, selecting the decision alternative with the best expected value usually leads to selection of the most preferred decision. a. True b. False 24. The expected utility is the utility of the expected monetary value. a. True b. False 25. A risk avoider is a decision maker who would choose a guaranteed payoff over a lottery with a superior expected payoff. a. True b. False 26. The utility function for a risk avoider typically shows a diminishing marginal return for money. a. True b. False 27. Given two decision makers, one a risk taker and the other a risk avoider, the risk avoider will show a diminishing marginal return for money. a. True b. False 28. When the expected utility approach and the expected value approach applied to monetary payoffs result in the same action, these are characteristics generally associated with a risk-neutral decision maker. a. True b. False Multiple Choice 29. The options from which a decision maker chooses a course of action are a. called the decision alternatives. b. not under the control of the decision maker. c. the same as the states of nature. d. None of these are correct. 30. States of nature a. are the possible outcomes for a chance event. b. can be selected by the decision maker. c. cannot be enumerated by the decision maker. d. None of these are correct. 31. A payoff a. is always measured in profit. b. is always measured in cost. c. exists for each pair of a decision alternative and a state of nature. d. exists for each state of nature. 32. Making a good decision a. requires probabilities for all states of nature. b. requires a clear understanding of decision alternatives, states of nature, and payoffs. c. implies that a desirable outcome will occur. d. All of these are correct. 33. A decision tree a. presents all decision alternatives first and follows them with all states of nature. b. presents all states of nature first and follows them with all decision alternatives. c. alternates the decision alternatives and states of nature. d. arranges decision alternatives and states of nature in their natural chronological order. 34. Which of the following methods for decision making best protects the decision maker from undesirable results? a. the optimistic approach b. the conservative approach c. minimum regret d. minimax regret 35. Sensitivity analysis a. considers how sensitive the decision maker is to risk. b. considers how changes in the number of states of nature can impact the recommended decision. c. considers how changes in various aspects of the problem affect the recommended decision alternative. d. None of these are correct. 36. To find the expected value of sample information (EVSI), a. use prior and sample information probabilities to calculate revised probabilities. b. use indicator probabilities to calculate prior probabilities. c. use sample information to revise the sample information probabilities. d. None of these are correct. 37. If P(high) = 0.3, P(low) = 0.7, P(favorable | high) = 0.9, and P(unfavorable | low) = 0.6, then P(favorable) = a. 0.10. b. 0.27. c. 0.30. d. 0.55. 38. The efficiency of sample information is a. EVSI*(100%). b. EVSI/EVPI*(100%). c. EVwoSI/EVwoPI*(100%). d. EVwSI/EVwoSI*(100%). 39. Decision tree probabilities refer to the probability of a. finding the optimal strategy. b. the decision being made. c. overlooked choices. d. an uncertain event occurring. 40. For a maximization problem, the conservative approach is often referred to as the a. minimax approach. b. maximin approach. c. maximax approach. d. minimin approach. 41. For a minimization problem, the optimistic approach is often referred to as the a. minimax approach. b. maximin approach. c. maximax approach. d. minimin approach. 42. For a maximization problem, the optimistic approach is often referred to as the a. minimax approach. b. maximin approach. c. maximax approach. d. minimin approach. 43. For a minimization problem, the conservative approach is often referred to as the a. minimax approach. b. maximin approach. c. maximax approach. d. minimin approach. 44. In an influence diagram, decision nodes are represented by a. circles or ovals. b. squares or rectangles. c. diamonds. d. triangles. 45. Which of the following approaches to decision making requires knowledge of the probabilities of the states of nature? a. minimax regret b. maximin c. expected value d. conservative 46. Decision tree probabilities are primarily used to a. analyze more complex problems and to identify an optimal sequence of decisions. b. analyze less complex problems while identifying the optimal sequence of decisions. c. find overlooked choices to the problem. d. None of these are correct. 47. Which of the following is NOT an advantage of using decision tree analysis? a. the ability to see clearly what decisions must be made b. the ability to see clearly in what sequence the decisions must occur c. the ability to see clearly the interdependence of decisions d. the ability to see clearly the future outcome of a decision 48. A decision tree provides a. the only method for analyzing decisions. b. a deterministic approach to decision analysis. c. the absolute value of the decision. d. an objective way of determining the relative value of each decision alternative. 49. The difference between the expected value of an optimal strategy based on sample information and the "best" expected value without any sample information is called the a. information sensitivity. b. expected value of sample information. c. expected value of perfect information. d. efficiency of sample information. 50. The purchase of insurance and lottery tickets shows that people make decisions based on a. expected value. b. sample information. c. utility. d. maximum likelihood. 51. The expected utility approach a. does not require probabilities. b. leads to the same decision as the expected value approach. c. is most useful when excessively large or small payoffs are possible. d. requires a decision tree. 52. Utility reflects the decision maker's attitude toward a. probability and profit. b. profit, loss, and risk. c. risk and regret. d. probability and regret. 53. The probability for which a decision maker cannot choose between a certain amount and a lottery based on that probability is the a. indifference probability. b. lottery probability. c. uncertain probability. d. utility probability. 54. A decision maker has chosen 0.4 as the probability for which he cannot choose between a certain loss of 10,000 and the lottery p(25,000) + (1  p)(5000). If the utility of 25,000 is 0 and of 5000 is 1, then the utility of 10,000 is a. 0.5. b. 0.6. c. 0.4. d. 4. 55. When the decision maker prefers a guaranteed payoff value that is smaller than the expected value of the lottery, the decision maker is a(n) a. risk avoider. b. risk taker. c. optimist. d. optimizer. 56. A decision maker whose utility function graphs as a straight line is a. conservative. b. a risk taker. c. risk neutral. d. a risk avoider. 57. When the utility function for a risk-neutral decision maker is graphed (with monetary value on the horizontal axis and utility on the vertical axis), the function appears as a(n) a. convex curve. b. concave curve. c. 'S' curve. d. straight line. Subjective Short Answer 58. East West Distributing is in the process of trying to determine where it should schedule next year's production of a popular line of kitchen utensils that it distributes. Manufacturers in four different countries have submitted bids to East West. However, a pending trade bill in Congress will greatly affect the cost to East West due to proposed tariffs, favorable trading status, etc. After careful analysis, East West has determined the following cost breakdown for the four manufacturers (in $1000s) based on whether or not the trade bill passes: Bill Passes Bill Fails Country A 260 210 Country B 320 160 Country C 240 240 Country D 275 210 a. If East West estimates that there is a 40% chance of the bill passing, which country should it choose for manufacturing? b. Over what range of values for the "bill passing" will the solution in part (a) remain optimal? 59. Super Cola is also considering the introduction of a root beer drink. The company thinks the probability that the product will be a success is 0.6. The payoff table is as follows: Success (s1) Failure (s2) Produce (d1) $250,000 −$300,000 Do not produce (d2) − 50,000 − 20,000 The company has a choice of two research firms to obtain information for this product. Stanton Marketing has market indicators I1 and I2 for which P(I1 | s1) = 0.7 and P(I1 | s2) = 0.4. New World Marketing has indicators J1 and J2 for which P(J1 | s1) = 0.6 and P(J1 | s2) = 0.3. a. What is the optimal decision if neither firm is used? Over what probability of success range is this decision optimal? b. What is the EVPI? c. Find the EVSIs and efficiencies for Stanton and New World. d. If both firms charge $5,000, which firm should be hired? e. If Stanton charges $10,000 and New World charges $4000, which firm should Super Cola hire? 60. Dollar Department Stores has just acquired the chain of Wenthrope and Sons Custom Jewelers. Dollar has received an offer from Harris Diamonds to purchase the Wenthrope store on Grove Street for $120,000. Dollar has determined probability estimates of the store's future profitability, based on economic outcomes, as: P($80,000) = 0.2, P($100,000) = 0.3, P($120,000) = 0.1, and P($140,000) = 0.4. a. Should Dollar sell the store on Grove Street? b. What is the EVPI? c. Dollar can have an economic forecast performed, costing $10,000, that produces indicators I1 and I2, for which P(I1 | 80,000) = 0.1; P(I1 | 100,000) = 0.2; P(I1 | 120,000) = 0.6; P(I1 | 140,000) = 0.3. Should Dollar purchase the forecast? 61. An appliance dealer must decide how many (if any) new microwave ovens to order for next month. The ovens cost $220 and sell for $300. Because the oven company is coming out with a new product line in two months, any ovens not sold next month will have to be sold at the dealer's half price clearance sale. Additionally, the appliance dealer feels he suffers a loss of $25 for every oven demanded when he is out of stock. On the basis of past months' sales data, the dealer estimates the probabilities of monthly demand (D) for 0, 1, 2, or 3 ovens to be 0.3, 0.4, 0.2, and 0.1, respectively. The dealer is considering conducting a telephone survey on customers' attitudes towards microwave ovens. The results of the survey will either be favorable (F), unfavorable (U), or no opinion (N). The dealer's probability estimates for the survey results based on the number of units demanded are: P(F | D = 0) = 0.1 P(F | D = 2) = 0.3 P(U | D = 0) = 0.8 P(U | D = 2) = 0.1 P(F | D = 1) = 0.2 P(F | D = 3) = 0.9 P(U | D = 1) = 0.3 P(U | D = 3) = 0.1 a. What is the dealer's optimal decision without conducting the survey? b. What is the EVPI? c. Based on the survey results, what is the optimal decision strategy for the dealer? d. What is the maximum amount he should pay for this survey? 62. Lakewood Fashions must decide how many lots of assorted ski wear to order for its three stores. Information on pricing, sales, and inventory costs has led to the following payoff table, in thousands. Show a regret table. Demand Order Size Low Medium High 1 lot 12 15 15 2 lots 9 25 35 3 lots 6 35 60 a. What decision should be made by the optimist? b. What decision should be made by the conservative? c. What decision should be made using minimax regret? 63. The table shows both prospective profits and losses for a company, depending on what decision is made and what state of nature occurs. Use the information to determine what the company should do. Show your work (regret table). State of Nature Decision s1 s2 s3 d1 30 80 30 d2 100 30 40 d3 80 10 120 d4 20 20 20 a. If an optimistic strategy is used. b. If a conservative strategy is used. c. If minimax regret is the strategy. 64. A decision maker has developed the following decision tree. How sensitive is the choice between N and P to the probabilities of states of nature U and V, and which would you choose? 65. If p is the probability of Event 1 and (1 − p) is the probability of Event 2, for what values of p would you choose A? B? C? Values in the table are payoffs. Choice/Event Event 1 Event 2 A 0 20 B 4 16 C 8 0 66. Fold back this decision tree. Clearly state the decision strategy you determine. 67. Use graphical sensitivity analysis to determine the range of values of the probability of state of nature s1 over which each of the decision alternatives has its largest expected value. State of Nature Decision s1 s2 d1 8 10 d2 4 16 d3 10 0 68. A paint company has three sources for buying bright red pigment for its paints: Vietnam, Taiwan, or Thailand. Unfortunately, the pigment is made from a bush whose annual growth is heavily dependent upon the amount of rainfall during the growing season. The tables below show probabilities and prices for wet, dry, and normal growing seasons. Probabilities Wet Dry Normal Vietnam 0.5 0.2 0.3 Taiwan 0.6 0.3 0.1 Thailand 0.4 0.4 0.2 Price/Pound ($) Wet Dry Normal Vietnam 0.95 1.10 1.00 Taiwan 0.85 1.20 0.98 Thailand 0.90 1.15 1.05 What country should the company select, and what is the expected value (price) associated with it? 69. A regional fast‑food restaurant is considering an expansion program. The major factor influencing the success of such a program is the future level of interest rates. It is estimated that there is a 20% chance that interest rates will increase by 2 percentage points, a 50% chance that they will remain the same, and a 30% chance that they will decrease by 2 percentage points. The alternatives they are considering and possible payoffs are shown in the table below. Which alternative is best, based on expected value? Rates up Rates Rates down 2% unchanged 2% Build 50 restaurants –$200,000 $50,000 $150,000 Build 25 restaurants –$115,000 $26,000 $80,000 Do nothing –$70,000 0 $5,000 70. A chemical company is trying to decide whether to build a pilot plant now for a new chemical process or to build the full plant now. If it builds a pilot plant now, it could expand later to a full plant or license the plant to another company. It would cost $2 million to build the pilot plant and another $2 million later to expand it. If the company builds the full plant now, it would cost $3.5 million to construct. The returns the company expects to get from the full production plant depend on the market. There is a 60% chance the market will be robust, a 30% chance it will remain stable, and a 10% chance it will become stagnate. The returns are estimated to be $5 million if it is robust, $3 million if it is stable, and $1 million if it is stagnate. Before the company expands the pilot plant, it plans to conduct a comprehensive study. Based on past experience, it expects the study to report a 60% chance of favorable outcome for expansion and a 40% unfavorable chance. In either case, it will have to decide whether to expand to a full plant or license the pilot plant. If the report is favorable and the company licenses it, the company expects to get $3 million. However, if the report is unfavorable and the company licenses it, the company will only get $1 million. Develop a decision tree for this problem and determine the optimal decision strategy. 71. A manufacturing company is considering expanding its production capacity to meet a growing demand for its product line of air fresheners. The alternatives are to build a new plant, expand the old plant, or do nothing. The marketing department estimates a 35% probability of a market upturn, a 40% probability of a stable market, and a 25% probability of a market downturn. Georgia Swain, the firm's capital appropriations analyst, estimates the following annual returns for these alternatives: Market Upturn Stable Market Market Downturn Build new plant $690,000 $(130,000) $(150,000) Expand old plant 490,000 (45,000) (65,000) Do nothing 50,000 0 (20,000) a. Use a decision tree to analyze these decision alternatives. b. What should the company do? c. What returns will accrue to the company if your recommendation is followed? 72. Sunshine Manufacturing Company has developed a unique new product and must now decide between two facility plans. The first alternative is to build a large new facility immediately. The second alternative is to build a small plant initially and to consider expanding it to a larger facility three years later if the market has proven favorable. Marketing has provided the following probability estimates for a 10-year plan: First 3-Year Demand Next 7-Year Demand Probability Unfavorable Unfavorable 0.2 Unfavorable Favorable 0.0 Favorable Favorable 0.7 Favorable Unfavorable 0.1 If the small plant is expanded, the probability of demands over the remaining seven years is 7/8 for favorable and 1/8 for unfavorable. The accounting department has provided the payoff for each outcome. Demand Facility Plan Payoff Favorable, favorable 1 $5,000,000 Favorable, unfavorable 1 2,500,000 Unfavorable, unfavorable 1 1,000,000 Favorable, favorable 2—expanded 4,000,000 Favorable, unfavorable 2—expanded 100,000 Favorable, favorable 2—not expanded 1,500,000 Favorable, unfavorable 2—not expanded 500,000 Unfavorable, unfavorable 2—not expanded 300,000 Use these estimates to analyze Sunshine's facility decision. a. Perform a complete decision tree analysis. b. Recommend a strategy to Sunshine. c. Determine what payoffs will result from your recommendation. 73. A Pacific Northwest lumber company is considering the expansion of one of its mills. The question is whether to do it now or wait one year and reconsider. If it expands now, the major factors are the state of the economy and the level of interest rates. The combination of these two factors results in five possible situations. If it does not expand now, only the state of the economy is important and three conditions characterize the possibilities. The following table summarizes the situation: Probabilities Revenues Expand Very favorable 0.2 $80,000 Favorable 0.2 $60,000 Neutral 0.1 $20,000 Unfavorable 0.3 –$20,000 Very unfavorable 0.2 –$30,000 Don't expand Expansion 0.2 $50,000 Steady 0.5 $30,000 Contraction 0.3 $10,000 a. Draw the decision tree for this problem. b. What is the expected value for expanding? c. What is the expected value for not expanding? d. Based on expected value, what should the company’s decision(s) be? 74. For the payoff table below, the decision maker will use P(s1) = 0.15, P(s2) = 0.5, and P(s3) = 0.35. State of Nature Decision s1 s2 s3 d1 5000 1000 10,000 d2 15,000 2000 40,000 a. What alternative would be chosen according to expected value? b. For a lottery having a payoff of 40,000 with probability p and 15,000 with probability (1  p), the decision maker expressed the following indifference probabilities: Payoff Probability 10,000 0.85 1000 0.60 2000 0.53 5000 0.50 Let U(40,000) = 10 and U(15,000) = 0 and find the utility value for each payoff. c. What alternative would be chosen according to expected utility? 75. A decision maker who is considered to be a risk taker is faced with this set of probabilities and payoffs. State of Nature Decision s1 s2 s3 d1 5 10 20 d2 25 0 50 d3 50 10 80 Probability 0.30 0.35 0.35 For the lottery p(80) + (1  p)(50), this decision maker has assessed the following indifference probabilities: Payoff Probability 50 0.60 20 0.35 10 0.25 5 0.22 0 0.20 10 0.18 25 0.10 Rank the decision alternatives on the basis of expected value and on the basis of expected utility. 76. Three decision makers have assessed utilities for the problem whose payoff table appears below. State of Nature Decision s1 s2 s3 d1 500 100 400 d2 200 150 100 d3 100 200 300 Probability 0.2 0.6 0.2 Indifference Probability for Person Payoff A B C 300 0.95 0.68 0.45 200 0.94 0.64 0.32 150 0.91 0.62 0.28 100 0.89 0.60 0.22 100 0.75 0.45 0.10 a. Plot the utility function for each decision maker. b. Characterize each decision maker's attitude toward risk. c. Which decision will each person prefer? 77. A decision maker has the following utility function: Payoff Indifference Probability 200 1.00 150 0.95 50 0.75 0 0.60 50 0 What is the risk premium for the payoff of 50? ANSWER: EV = 0.75(200) + 0.25(50) = 137.50 Risk premium is 137.50  50 = 87.50. POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.13.07 - 13.7 NATIONAL STANDARDS: United States - BUSPROG: Analytic TOPICS: 13.7 Utility Theory KEYWORDS: Bloom's: Analyze 78. Determine decision strategies based on expected value and on expected utility for this decision tree. Use the following utility function: Payoff Indifference Probability 500 1.00 350 0.89 300 0.84 180 0.60 100 0.43 40 0.20 20 0.13 0 0 79. Burger Prince Restaurant is considering the purchase of a $100,000 fire insurance policy. The fire statistics indicate that in a given year the probability of property damage in a fire is as follows: Fire Damage $100,000 $75,000 $50,000 $25,000 $10,000 $0 Probability 0.006 0.002 0.004 0.003 0.005 0.980 a. If Burger Prince was risk neutral, how much would it be willing to pay for fire insurance? b. If Burger Prince has the utility values given below, approximately how much would it be willing to pay for fire insurance? Loss $100,000 $75,000 $50,000 $25,000 $10,000 $5,000 $0 Utility 0 30 60 85 95 99 100 80. Super Cola is considering the introduction of a new eight-oz. root beer. The probability that the root beer will be a success is believed to equal 0.6. The payoff table is as follows: Success (s1) Failure (s2) Produce $250,000 $300,000 Do not produce $50,000 $20,000 Company management has determined the following utility values: Amount $250,000 $20,000 $50,000 $300,000 Utility 100 60 55 0 a. Is the company a risk taker, risk averse, or risk neutral? b. What is Super Cola's optimal decision? 81. Chez Paul is contemplating either opening another restaurant or expanding its existing location. The payoff table for these two decisions is as follows: State of Nature Decision s1 s2 s3 New restaurant $80,000 $20,000 $160,000 Expand 40,000 20,000 100,000 Paul has calculated the indifference probability for the lottery having a payoff of $160,000 with probability p and $80,000 with probability (1 p) as follows: Amount Indifference Probability (p) $ 40,000 0.4 20,000 0.7 100,000 0.9 a. Is Paul a risk avoider, a risk taker, or risk neutral? b. Suppose Paul has defined the utility of $80,000 to be 0 and the utility of $160,000 to be 80. What would be the utility values for $40,000, $20,000, and $100,000 based on the indifference probabilities? c. Suppose P(s1) = 0.4, P(s2) = 0.3, and P(s3) = 0.3. Which decision should Paul make? Compare with the decision using the expected value approach. 82. The Dollar Department Store chain has the opportunity of acquiring 3, 5, or 10 leases from the bankrupt Granite Variety Store chain. Dollar estimates the profit potential of the leases depends on the state of the economy over the next five years. There are four possible states of the economy as modeled by Dollar Department Stores, and its president estimates P(s1) = 0.4, P(s2) = 0.3, P(s3) = 0.1, and P(s4) = 0.2. The utility has also been estimated. Given the payoffs (in $1,000,000s) and utility values below, which decision should Dollar make? Payoff Table State of the Economy over the Next 5 Years Decision s1 s2 s3 s4 d1 — buy 10 leases 10 5 0 20 d2 — buy 5 leases 5 0 1 10 d3 — buy 3 leases 2 1 0 1 d4 — do not buy 0 0 0 0 Utility Table Payoff (in $1,000,000s) +10 +5 +2 0 1 10 20 Utility +10 +5 +2 0 1 20 50 83. Consider the following problem with four states of nature, three decision alternatives, and the following payoff table (in $s): The indifference probabilities for three individuals are as follows: Payoff Person 1 Person 2 Person 3 $ 2600 1.00 1.00 1.00 400 0.40 0.45 0.55 200 0.35 0.40 0.50 0 0.30 0.35 0.45 – 200 0.25 0.30 0.40 –1400 0 0 0 a. Classify each person as a risk avoider, risk taker, or risk neutral. b. For the payoff of $400, what premium will the risk avoider pay to avoid risk? What premium will the risk taker pay to have the opportunity of the high payoff? c. Suppose each state is equally likely. What are the optimal decisions for each of these three people? s1 s2 s3 s4 d1 200 2600 –1400 200 d2 0 200 – 200 200 d3 –200 400 0 200 84. Metropolitan Cablevision has the choice of using one of three DVR systems. Profits are believed to be a function of customer acceptance. The payoff to Metropolitan for the three systems is as follows: System Acceptance Level I II III High $150,000 $200,000 $200,000 Medium 80,000 20,000 80,000 Low 20,000 – 50,000 –100,000 The probabilities of customer acceptance for each system are as follows: System Acceptance Level I II III High 0.4 0.3 0.3 Medium 0.3 0.4 0.5 Low 0.3 0.3 0.2 The first vice president believes that the indifference probabilities for Metropolitan should be as follows: Amount Probability $150,000 0.90 80,000 0.70 20,000 0.50 – 50,000 0.25 The second vice president believes Metropolitan should assign the following utility values: Amount Utility $200,000 125 150,000 95 80,000 55 20,000 30 – 50,000 10 –100,000 0 a. Which vice president is a risk taker? Which one is risk averse? b. Which system will each vice president recommend? c. Which system would a risk-neutral vice president recommend? [Show More]

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