3-17 Kenneth Brown is the principal owner of Brown Oil, Inc. After quitting his university teaching job, Ken has been able to increase his annual salary by a factor of over 100. At the present time, Ken is forced to consider purchasing some more equipment for Brown Oil because of competition. His alternatives are shown in the following table:

For example, if Ken purchases a Sub 100 and if there is a favorable market, he will realize a profit of $300,000. On the other hand, if the market is unfavorable, Ken will suffer a loss of $200,000. But Ken has always been a very optimistic decision maker.

1. What type of decision is Ken facing?

2. What decision criterion should he use?

3. What alternative is best?

3-18 Although Ken Brown (discussed in Problem 3-17) is the principal owner of Brown Oil, his brother Bob is credited with making the company a financial success. Bob is vice president of finance. Bob attributes his success to his pessimistic attitude about business and the oil industry. Given the information from Problem 3-17, it is likely that Bob will arrive at a different decision. What decision criterion should Bob use, and what alternative will he select?

3-19 The Lubricant is an expensive oil newsletter to which many oil giants subscribe, including Ken Brown (see Problem 3-17 for details). In the last issue, the letter described how the demand for oil products would be extremely high. Apparently, the American consumer will continue to use oil products even if the price of these products doubles. Indeed, one of the articles in the Lubricant states that the chance of a favorable market for oil products was 70%, while the chance of an unfavorable market was only 30%. Ken would like to use these probabilities in determining the best decision.

1. What decision model should be used?

2. What is the optimal decision?

3. Ken believes that the $300,000 figure for the Sub 100 with a favorable market is too high. How much lower would this figure have to be for Ken to change his decision made in part (b)?

3-20 Mickey Lawson is considering investing some money that he inherited. The following payoff table gives the profits that would be realized during the next year for each of three investment alternatives Mickey is considering:

1. What decision would maximize expected profits?

2. What is the maximum amount that should be paid for a perfect forecast of the economy?

3-21 Develop an opportunity loss table for the investment problem that Mickey Lawson faces in Problem 3-20. What decision would minimize the expected opportunity loss? What is the minimum EOL?

3-22 Allen Young has always been proud of his personal investment strategies and has done very well over the past several years. He invests primarily in the stock market. Over the past several months, however, Allen has become very concerned about the stock market as a good investment. In some cases, it would have been better for Allen to have his money in a bank than in the market. During the next year, Allen must decide whether to invest $10,000 in the stock market or in a certificate of deposit (CD) at an interest rate of 9%. If the market is good, Allen believes that he could get a 14% return on his money. With a fair market, he expects to get an 8% return. If the market is bad, he will most likely get no return at all—in other words, the return would be 0%. Allen estimates that the probability of a good market is 0.4, the probability of a fair market is 0.4, and the probability of a bad market is 0.2, and he wishes to maximize his long-run average return.

1. Develop a decision table for this problem.

2. What is the best decision?

3-23 In Problem 3-22, you helped Allen Young determine the best investment strategy. Now, Allen is thinking about paying for a stock market newsletter. A friend of Allen said that these types of letters could predict very accurately whether the market would be good, fair, or poor. Then, based on these predictions, Allen could make better investment decisions.

1. What is the most that Allen would be willing to pay for a newsletter?

2. Allen now believes that a good market will give a return of only 11% instead of 14%. Will this information change the amount that Allen would be willing to pay for the newsletter? If your answer is yes, determine the most that Allen would be willing to pay, given this new information.

3-24 Today’s Electronics specializes in manufacturing modern electronic components. It also builds the equipment that produces the components. Phyllis Weinberger, who is responsible for advising the president of Today’s Electronics on electronic manufacturing equipment, has developed the following table concerning a proposed facility:

1. Develop an opportunity loss table.

2. What is the minimax regret decision?

3-25 Brilliant Color is a small supplier of chemicals and equipment that are used by some photographic stores to process 35mm film. One product that Brilliant Color supplies is BC-6. John Kubick, president of Brilliant Color, normally stocks 11, 12, or 13 cases of BC-6 each week. For each case that John sells, he receives a profit of $35. Like many photographic chemicals, BC-6 has a very short shelf life, so if a case is not sold by the end of the week, John must discard it. Since each case costs John $56, he loses $56 for every case that is not sold by the end of the week. There is a probability of 0.45 of selling 11 cases, a probability of 0.35 of selling 12 cases, and a probability of 0.2 of selling 13 cases.

1. Construct a decision table for this problem. Include all conditional values and probabilities in the table.

2. What is your recommended course of action?

3. If John is able to develop BC-6 with an ingredient that stabilizes it so that it no longer has to be discarded, how would this change your recommended course of action?

3-26 Megley Cheese Company is a small manufacturer of several different cheese products. One of the products is a cheese spread that is sold to retail outlets. Jason Megley must decide how many cases of cheese spread to manufacture each month. The probability that the demand will be six cases is 0.1, seven cases is 0.3, eight cases is 0.5, and nine cases is 0.1. The cost of every case is $45, and the price that Jason gets for each case is $95. Unfortunately, any cases not sold by the end of the month are of no value, due to spoilage. How many cases of cheese should Jason manufacture each month?

3-27 Farm Grown, Inc., produces cases of perishable food products. Each case contains an assortment of vegetables and other farm products. Each case costs $5 and sells for $15. If there are any cases not sold by the end of the day, they are sold to a large food processing company for $3 a case. The probability that daily demand will be 100 cases is 0.3, the probability that daily demand will be 200 cases is 0.4, and the probability that daily demand will be 300 cases is 0.3. Farm Grown has a policy of always satisfying customer demands. If its own supply of cases is less than the demand, it buys the necessary vegetables from a competitor. The estimated cost of doing this is $16 per case.

1. Draw a decision table for this problem.

2. What do you recommend?

3-28 In Problem 3-27, Farm Grown, Inc., has reason to believe the probabilities may not be reliable due to changing conditions. If these probabilities are ignored, what decision would be made using the optimistic criterion? What decision would be made using the pessimistic criterion?

3-29 Mick Karra is the manager of MCZ Drilling Products, which produces a variety of specialty valves for oil field equipment. Recent activity in the oil fields has caused demand to increase drastically, and a decision has been made to open a new manufacturing facility. Three locations are being considered, and the size of the facility would not be the same in each location. Thus, overtime might be necessary at times. The following table gives the total monthly cost (in $1,000s) for each possible location under each demand possibility. The probabilities for the demand levels have been determined to be 20% for low demand, 30% for medium demand, and 50% for high demand.

1. Which location would be selected based on the optimistic criterion?

2. Which location would be selected based on the pessimistic criterion?

3. Which location would be selected based on the minimax regret criterion?

4. Which location should be selected to minimize the expected cost of operation?

5. How much is a perfect forecast of the demand worth?

6. Which location would minimize the expected opportunity loss?

7. What is the expected value of perfect information in this situation?

3-30 Even though independent gasoline stations have been having a difficult time, Susan Solomon has been thinking about starting her own independent gasoline station. Susan’s problem is to decide how large her station should be. The annual returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline. After a careful analysis, Susan developed the following table:

For example, if Susan constructs a small station and the market is good, she will realize a profit of $50,000.

1. Develop a decision table for this decision.

2. What is the maximax decision?

3. What is the maximin decision?

4. What is the equally likely decision?

5. What is the criterion of realism decision? Use an $\alpha$ value of 0.8.

6. Develop an opportunity loss table.

7. What is the minimax regret decision?

3-31 Beverly Mills has decided to lease a hybrid car to save on gasoline expenses and to do her part to help keep the environment clean. The car she selected is available from only one dealer in the local area, but that dealer has several leasing options to accommodate a variety of driving patterns. All the leases are for 3 years and require no money at the time of signing the lease. The first option has a monthly cost of $330, a total mileage allowance of 36,000 miles (an average of 12,000 miles per year), and a cost of $0.35 per mile for any miles over 36,000. The following table summarizes each of the three lease options:

Beverly has estimated that, during the 3 years of the lease, there is a 40% chance she will drive an average of 12,000 miles per year, a 30% chance she will drive an average of 15,000 miles per year, and a 30% chance that she will drive 18,000 miles per year. In evaluating these lease options, Beverly would like to keep her costs as low as possible.

1. Develop a payoff (cost) table for this situation.

2. What decision would Beverly make if she were optimistic?

3. What decision would Beverly make if she were pessimistic?

4. What decision would Beverly make if she wanted to minimize her expected cost (monetary value)?

5. Calculate the expected value of perfect information for this problem.

3-32 Refer to the leasing decision facing Beverly Mills in Problem 3-31. Develop the opportunity loss table for this situation. Which option would be chosen based on the minimax regret criterion? Which alternative would result in the lowest expected opportunity loss?

3-33 The game of roulette is popular in many casinos around the world. In Las Vegas, a typical roulette wheel has the numbers 1–36 in slots on the wheel. Half of these slots are red, and the other half are black. In the United States, the roulette wheel typically also has the numbers 0 (zero) and 00 (double zero), and both of these are on the wheel in green slots. Thus, there are 38 slots on the wheel. The dealer spins the wheel and sends a small ball in the opposite direction of the spinning wheel. As the wheel slows, the ball falls into one of the slots, and that is the winning number and color. One of the bets available is simply red or black, for which the odds are 1 to 1. If the player bets on either red or black and that happens to be the winning color, the player wins the amount of her bet. For example, if the player bets $5 on red and wins, she is paid $5 and she still has her original bet. On the other hand, if the winning color is black or green when the player bets red, the player loses the entire bet.

1. What is the probability that a player who bets red will win the bet?

2. If a player bets $10 on red every time the game is played, what is the expected monetary value (expected win)?

3. In Europe, there is usually no 00 on the wheel, just the 0. With this type of game, what is the probability that a player who bets red will win the bet? If a player bets $10 on red every time in this game (with no 00), what is the expected monetary value?

4. Since the expected profit (win) in a roulette game is negative, why would a rational person play the game?

3-34 Refer to Problem 3-33 for details about the game of roulette. Another bet in a roulette game is called a “straight up” bet, which means that the player is betting that the winning number will be the number that she chose. In a game with 0 and 00, there is a total of 38 possible outcomes (the numbers 1 to 36 plus 0 and 00), and each of these has the same chance of occurring. The payout on this type of bet is 35 to 1, which means the player is paid 35 and gets to keep the original bet. If a player bets $10 on the number 7 (or any single number), what is the expected monetary value (expected win)?

3-35 The Technically Techno company has several patents for a variety of different flash memory devices that are used in computers, cell phones, and a variety of other things. A competitor has recently introduced a product based on technology very similar to something patented by Technically Techno last year. Consequently, Technically Techno has sued the other company for patent infringement. Based on the facts in the case as well as the record of the lawyers involved, Technically Techno believes there is a 40% chance that it will be awarded $300,000 if the lawsuit goes to court. There is a 30% chance that Technically Techno will be awarded only $50,000 if it goes to court and wins, and there is a 30% chance that Technically Techno will lose the case and be awarded nothing. The estimated cost of legal fees if Technically Techno goes to court is $50,000. However, the other company has offered to pay Technically Techno $75,000 to settle the dispute without going to court. The estimated legal cost of this would be only $10,000. If Technically Techno wished to maximize the expected gain, should it accept the settlement offer?

3-36 A group of medical professionals is considering the construction of a private clinic. If the medical demand is high (i.e., there is a favorable market for the clinic), the physicians could realize a net profit of $100,000. If the market is not favorable, they could lose $40,000. Of course, they don’t have to proceed at all, in which case there is no cost. In the absence of any market data, the physicians’ best guess is that there is a 50–50 chance the clinic will be successful. Construct a decision tree to help analyze this problem. What should the medical professionals do?

3-37 The physicians in Problem 3-36 have been approached by a market research firm that offers to perform a study of the market at a fee of $5,000. The market researchers claim their experience enables them to use Bayes’ Theorem to make the following statements of probability:

1. Develop a new decision tree for the medical professionals to reflect the options now open with the market study.

2. Use the EMV approach to recommend a strategy.

3. What is the expected value of sample information? How much might the physicians be willing to pay for a market study?

4. Calculate the efficiency of this sample information.

3-38 Jerry Smith is thinking about opening a bicycle shop in his hometown. Jerry loves to take his own bike on 50-mile trips with his friends, but he believes that any small business should be started only if there is a good chance of making a profit. Jerry can open a small shop, a large shop, or no shop at all. The profits will depend on the size of the shop and whether the market is favorable or unfavorable for his products. Because there will be a 5-year lease on the building that Jerry is thinking about using, he wants to make sure that he makes the correct decision. Jerry is also thinking about hiring his old marketing professor to conduct a marketing research study. If the study is conducted, the study could be favorable (i.e., predicting a favorable market) or unfavorable (i.e., predicting an unfavorable market). Develop a decision tree for Jerry.

3-39 Jerry Smith (see Problem 3-38) has done some analysis about the profitability of the bicycle shop. If Jerry builds the large bicycle shop, he will earn $60,000 if the market is favorable, but he will lose $40,000 if the market is unfavorable. The small shop will return a $30,000 profit in a favorable market and a $10,000 loss in an unfavorable market. At the present time, he believes that there is a 50–50 chance that the market will be favorable. His old marketing professor will charge him $5,000 for the marketing research. It is estimated that there is a 0.6 probability that the survey will be favorable. Furthermore, there is a 0.9 probability that the market will be favorable given a favorable outcome from the study. However, the marketing professor has warned Jerry that there is only a probability of 0.12 of a favorable market if the marketing research results are not favorable. Jerry is confused.

1. Should Jerry use the marketing research?

2. Jerry, however, is unsure the 0.6 probability of a favorable marketing research study is correct. How sensitive is Jerry’s decision to this probability value? How far can this probability value deviate from 0.6 without causing Jerry to change his decision?

3-40 Bill Holliday is not sure what he should do. He can build a quadplex (i.e., a building with four apartments), build a duplex, gather additional information, or simply do nothing. If he gathers additional information, the results could be either favorable or unfavorable, but it would cost him $3,000 to gather the information. Bill believes that there is a 50–50 chance that the information will be favorable. If the rental market is favorable, Bill will earn $15,000 with the quadplex or $5,000 with the duplex. Bill doesn’t have the financial resources to do both. With an unfavorable rental market, however, Bill could lose $20,000 with the quadplex or $10,000 with the duplex. Without gathering additional information, Bill estimates that the probability of a favorable rental market is 0.7. A favorable report from the study would increase the probability of a favorable rental market to 0.9. Furthermore, an unfavorable report from the additional information would decrease the probability of a favorable rental market to 0.4. Of course, Bill could forget all of these numbers and do nothing. What is your advice to Bill?

3-41 Peter Martin is going to help his brother who wants to open a food store. Peter initially believes that there is a 50–50 chance that his brother’s food store would be a success. Peter is considering doing a market research study. Based on historical data, there is a 0.8 probability that the marketing research will be favorable given a successful food store. Moreover, there is a 0.7 probability that the marketing research will be unfavorable given an unsuccessful food store.

1. If the marketing research is favorable, what is Peter’s revised probability of a successful food store for his brother?

2. If the marketing research is unfavorable, what is Peter’s revised probability of a successful food store for his brother?

3. If the initial probability of a successful food store is 0.60 (instead of 0.50), find the probabilities in parts (a) and (b).

3-42 Mark Martinko has been a class A racquetball player for the past 5 years, and one of his biggest goals is to own and operate a racquetball facility. Unfortunately, Mark thinks that the chance of a successful racquetball facility is only 30%. Mark’s lawyer has recommended that he employ one of the local marketing research groups to conduct a survey concerning the success or failure of a racquetball facility. There is a 0.8 probability that the research will be favorable given a successful racquetball facility. In addition, there is a 0.7 probability that the research will be unfavorable given an unsuccessful facility. Compute revised probabilities of a successful racquetball facility given a favorable and given an unfavorable survey.

3-43 A financial advisor has recommended two possible mutual funds for investment: Fund A and Fund B. The return that will be achieved by each of these depends on whether the economy is good, fair, or poor. A payoff table has been constructed to illustrate this situation:

1. Draw the decision tree to represent this situation.

2. Perform the necessary calculations to determine which of the two mutual funds is better. Which one should you choose to maximize the expected value?

3. Suppose there is a question about the return of Fund A in a good economy. It could be higher or lower than $10,000. What value for this would cause a person to be indifferent between Fund A and Fund B (i.e., the EMVs would be the same)?

3-44 Jim Sellers is thinking about producing a new type of electric razor for men. If the market were favorable, he would get a return of $100,000, but if the market for this new type of razor were unfavorable, he would lose $60,000. Since Ron Bush is a good friend of Jim Sellers, Jim is considering the possibility of using Bush Marketing Research to gather additional information about the market for the razor. Ron has suggested that Jim use either a survey or a pilot study to test the market. The survey would be a sophisticated questionnaire administered to a test market. It will cost $5,000. Another alternative is to run a pilot study. This would involve producing a limited number of the new razors and trying to sell them in two cities that are typical of American cities. The pilot study is more accurate but is also more expensive. It will cost $20,000. Ron Bush has suggested that it would be a good idea for Jim to conduct either the survey or the pilot before Jim makes the decision concerning whether to produce the new razor. But Jim is not sure if the value of the survey or the pilot is worth the cost.

Jim estimates that the probability of a successful market without performing a survey or pilot study is 0.5. Furthermore, the probability of a favorable survey result given a favorable market for razors is 0.7, and the probability of a favorable survey result given an unsuccessful market for razors is 0.2. In addition, the probability of an unfavorable pilot study given an unfavorable market is 0.9, and the probability of an unsuccessful pilot study result given a favorable market for razors is 0.2.

1. Draw the decision tree for this problem without the probability values.

2. Compute the revised probabilities needed to complete the decision, and place these values in the decision tree.

3. What is the best decision for Jim? Use EMV as the decision criterion.

3-45 Jim Sellers has been able to estimate his utility for a number of different values. He would like to use these utility values in making the decision in Problem 3-44: $U\left(\mathrm{-}\$80,000\right)=0, U\left(\mathrm{-}\$65,000\right)=0.5,$ $U\left(\mathrm{-}\$60,000\right)=0.55, U\left(\mathrm{-}\$20,000\right)=0.7,$ $U\left(\mathrm{-}\$5,000\right)=0.8, U\left(\$0\right)=0.81, U\left(\$80,000\right)=$ $0.9, U\left(\$95,000\right)=0.95,\text{ and }U\left(\$100,000\right)=1.$

Resolve Problem 3-44 using utility values. Is Jim a risk avoider?

3-46 Two states of nature exist for a particular situation: a good economy and a poor economy. An economic study may be performed to obtain more information about which of these will actually occur in the coming year. The study may forecast either a good economy or a poor economy. Currently there is a 60% chance that the economy will be good and a 40% chance that it will be poor. In the past, whenever the economy was good, the economic study predicted it would be good 80% of the time. (The other 20% of the time the prediction was wrong.) In the past, whenever the economy was poor, the economic study predicted it would be poor 90% of the time. (The other 10% of the time the prediction was wrong.)

1. Use Bayes’ Theorem and find the following:

   • $P\left(\text{good}\text{economy}|\text{p}\text{r}\text{e}\text{d}\text{i}\text{c}\text{t}\text{i}\text{o}\text{n}\text{o}\text{f}\text{g}\text{o}\text{o}\text{d}\text{e}\text{c}\text{o}\text{n}\text{o}\text{m}\text{y}\right)$

   • $P\left(\text{poor}\text{economy}|\text{p}\text{r}\text{e}\text{d}\text{i}\text{c}\text{t}\text{i}\text{o}\text{n}\text{o}\text{f}\text{g}\text{o}\text{o}\text{d}\text{e}\text{c}\text{o}\text{n}\text{o}\text{m}\text{y}\right)$

   • $P\left(\text{good}\text{economy}|\text{p}\text{r}\text{e}\text{d}\text{i}\text{c}\text{t}\text{i}\text{o}\text{n}\text{o}\text{f}\text{p}\text{o}\text{o}\text{r}\text{e}\text{c}\text{o}\text{n}\text{o}\text{m}\text{y}\right)$

   • $P\left(\text{poor}\text{economy}|\text{p}\text{r}\text{e}\text{d}\text{i}\text{c}\text{t}\text{i}\text{o}\text{n}\text{o}\text{f}\text{p}\text{o}\text{o}\text{r}\text{e}\text{c}\text{o}\text{n}\text{o}\text{m}\text{y}\right)$

2. Suppose the initial (prior) probability of a good economy is 70% (instead of 60%) and the initial probability of a poor economy is 30% (instead of 40%). Find the posterior probabilities in part (a) based on these new values.

3-47 The Long Island Life Insurance Company sells a term life insurance policy. If the policy holder dies during the term of the policy, the company pays $100,000. If the person does not die, the company pays out nothing, and there is no further value to the policy. The company uses actuarial tables to determine the probability that a person with certain characteristics will die during the coming year. For a particular individual, it is determined that there is a 0.001 chance that the person will die in the next year and a 0.999 chance that the person will live and the company will pay out nothing. The cost of this policy is $200 per year. Based on the EMV criterion, should the individual buy this insurance policy? How would utility theory help explain why a person would buy this insurance policy?

3-48 In Problem 3-37, you helped the medical professionals analyze their decision using expected monetary value as the decision criterion. This group has also assessed its utility for money: $U\left(\mathrm{-}\$45,000\right)=0,$ $U\left(\mathrm{-}\$40,000\right)=0.1,U\left(\mathrm{-}\$5,000\right)=0.7,U\left(\$0\right)=$ $0.9,U\left(\$95,000\right)=0.99,$ and $U\left(\$100,000\right)=1.$ Use expected utility as the decision criterion, and determine the best decision for the medical professionals. Are the medical professionals risk seekers or risk avoiders?

3-49 In this chapter, a decision tree was developed for John Thompson (see Figure 3.5 for the complete decision tree analysis). After completing the analysis, John was not completely sure that he is indifferent to risk. After going through a number of standard gambles, John was able to assess his utility for money. Here are some of the utility assessments:

$U\left(\mathrm{-}\$190,000\right)=0,U\left(\mathrm{-}\$180,000\right)=0.05,$ $U\left(\mathrm{-}\$30,000\right)=0.10,U\left(\mathrm{-}\$20,000\right)=0.15,$ $U\left(\mathrm{-}\$10,000\right)=0.2,U\left(\$0\right)=0.3,U\left(\$90,000\right)=$ $0.15, U\left(\$100,000\right)=0.6,U\left(\$190,000\right)=0.95,$

and $U\left(\$200,000\right)=\mathrm{1.0.}$ If John maximizes his expected utility, does his decision change?

3-50 In the past few years, the traffic problems in Lynn McKell’s hometown have gotten worse. Now, Broad Street is congested about half the time. The normal travel time to work for Lynn is only 15 minutes when Broad Street is used and there is no congestion. With congestion, however, it takes Lynn 40 minutes to get to work. If Lynn decides to take the expressway, it will take 30 minutes, regardless of the traffic conditions. Lynn’s utility for travel time is $U\left(15 \text{minutes}\right)=0.9, U\left(30 \text{minutes}\right)=0.7,$ and $U\left(40 \text{minutes}\right)=\mathrm{0.2.}$

1. Which route will minimize Lynn’s expected travel time?

2. Which route will maximize Lynn’s utility?

3. When it comes to travel time, is Lynn a risk seeker or a risk avoider?

3-51 Coren Chemical, Inc., develops industrial chemicals that are used by other manufacturers to produce photographic chemicals, preservatives, and lubricants. One of their products, K-1000, is used by several photographic companies to make a chemical that is used in the film-developing process. To produce K-1000 efficiently, Coren Chemical uses the batch approach, in which a certain number of gallons is produced at one time. This reduces setup costs and allows Coren Chemical to produce K-1000 at a competitive price. Unfortunately, K-1000 has a very short shelf life of about 1 month.

Coren Chemical produces K-1000 in batches of 500 gallons, 1,000 gallons, 1,500 gallons, and 2,000 gallons. Using historical data, David Coren was able to determine that the probability of selling 500 gallons of K-1000 is 0.2. The probabilities of selling 1,000, 1,500, and 2,000 gallons are 0.3, 0.4, and 0.1, respectively. The question facing David is how many gallons to produce of K-1000 in the next batch run. K-1000 sells for $20 per gallon. Manufacturing cost is $12 per gallon, and handling costs and warehousing costs are estimated to be $1 per gallon. In the past, David has allocated advertising costs to K-1000 at $3 per gallon. If K-1000 is not sold after the batch run, the chemical loses much of its important properties as a developer. It can, however, be sold at a salvage value of $13 per gallon. Furthermore, David has guaranteed to his suppliers that there will always be an adequate supply of K-1000. If David does run out, he has agreed to purchase a comparable chemical from a competitor at $25 per gallon. David sells all of the chemical at $20 per gallon, so his shortage means that David loses the $5 to buy the more expensive chemical.

1. Develop a decision tree of this problem.

2. What is the best solution?

3. Determine the expected value of perfect information.

3-52 The Jamis Corporation is involved with waste management. During the past 10 years, it has become one of the largest waste disposal companies in the Midwest, serving primarily Wisconsin, Illinois, and Michigan. Bob Jamis, president of the company, is considering the possibility of establishing a waste treatment plant in Mississippi. From past experience, Bob believes that a small plant in northern Mississippi would yield a $500,000 profit, regardless of the market for the facility. The success of a medium-sized waste treatment plant would depend on the market. With a low demand for waste treatment, Bob expects a $200,000 return. A medium demand would yield a $700,000 return in Bob’s estimation, and a high demand would return $800,000. Although a large facility is much riskier, the potential return is much greater. With a high demand for waste treatment in Mississippi, the large facility should return a million dollars. With a medium demand, the large facility will return only $400,000. Bob estimates that the large facility would be a big loser if there were a low demand for waste treatment. He estimates that he would lose approximately $200,000 with a large treatment facility if demand were indeed low. Looking at the economic conditions for the upper part of the state of Mississippi and using his experience in the field, Bob estimates that the probability of a low demand for treatment plants is 0.15. The probability of a medium demand for a waste treatment facility is approximately 0.40, and the probability of a high demand for a waste treatment facility is 0.45.

Because of the large potential investment and the possibility of a loss, Bob has decided to hire a market research team that is based in Jackson, Mississippi. This team will perform a survey to get a better feeling for the probability of a low, medium, or high demand for a waste treatment facility. The cost of the survey is $50,000. To help Bob determine whether to go ahead with the survey, the marketing research firm has provided Bob with the following information:

As you see, the survey could result in three possible outcomes. Low survey results would mean that a low demand is likely. In a similar fashion, medium survey results or high survey results would mean a medium or a high demand, respectively. What should Bob do?

3-53 Mary is considering opening a new grocery store in town. She is evaluating three sites: downtown, the mall, and out at the busy traffic circle. Mary calculated the value of successful stores at these locations as follows: downtown, $250,000; the mall, $300,000; the circle, $400,000. Mary calculated the losses if unsuccessful to be $100,000 at either downtown or the mall and $200,000 at the circle. Mary figures her chance of success to be 50% downtown, 60% at the mall, and 75% at the traffic circle.

1. Draw a decision tree for Mary and select her best alternative.

2. Mary has been approached by a marketing research firm that offers to study the area to determine if another grocery store is needed. The cost of this study is $30,000. Mary believes there is a 60% chance that the survey results will be positive (show a need for another grocery store). $\text{SRP}=$survey results positive, $\text{SRN}=$ survey results negative, $\text{SD}=$success downtown, $\text{SM}=$success at mall, $\text{SC}=$success at circle, $\text{SD}\prime =$don’t succeed downtown, and so on. For studies of this nature:

   • $P\left(\text{SRP}|\text{s}\text{u}\text{c}\text{c}\text{e}\text{s}\text{s}\right)=0.7,$

   • $P\left(\text{SRN}|\text{s}\text{u}\text{c}\text{c}\text{e}\text{s}\text{s}\right)=0.3,$

   • $P\left(\text{SRP}|\text{n}\text{o}\text{t}\text{s}\text{u}\text{c}\text{c}\text{e}\text{s}\text{s}\right)=0.2,$ and

   • $P\left(\text{SRN}|\text{n}\text{o}\text{t}\text{s}\text{u}\text{c}\text{c}\text{e}\text{s}\text{s}\right)=\mathrm{0.8.}$

   Calculate the revised probabilities for success (and not success) for each location, depending on survey results.

3. How much is the marketing research worth to Mary? Calculate the EVSI.

3-54 Sue Reynolds has to decide if she should get information (at a cost of $20,000) to help her decide whether to invest in a retail store. If she gets the information, there is a 0.6 probability that the information will be favorable and a 0.4 probability that the information will not be favorable. If the information is favorable, there is a 0.9 probability that the store will be a success. If the information is not favorable, the probability of a successful store is only 0.2. Without any information, Sue estimates that the probability of a successful store will be 0.6. A successful store will give a return of $100,000. If the store is built but is not successful, Sue will see a loss of $80,000. Of course, she could always decide not to build the retail store.

1. What do you recommend?

2. What impact would a 0.7 probability of obtaining favorable information have on Sue’s decision? The probability of obtaining unfavorable information would be 0.3.

3. Sue believes that the probabilities of a successful and an unsuccessful retail store, given favorable information, might be 0.8 and 0.2, respectively, instead of 0.9 and 0.1, respectively. What impact, if any, would this have on Sue’s decision and the best EMV?

4. Sue had to pay $20,000 to get information. Would her decision change if the cost of the information increased to $30,000?

5. Using the data in this problem and the following utility table, compute the expected utility. Is this the curve of a risk seeker or a risk avoider?

   MONETARY VALUE	UTILITY
   $100,000	1
   $80,000	0.4
   $0	0.2
   –$20,000	0.1
   –$80,000	0.05
   –$100,000	0

6. Compute the expected utility given the following utility table. Does this utility table represent a risk seeker or a risk avoider?

   MONETARY VALUE	UTILITY
   $100,000	1
   $80,000	0.9
   $0	0.8
   –$20,000	0.6
   –$80,000	0.4
   –$100,000	0