1) 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:

STATE OF NATURE

DECISION ALTERNATIVE GOOD ECONOMY POOR ECONOMY Stock market 80,000 -20,000 Bonds 30,000 20,000 CDs 23,000 23,000 Probability 0.5 0.5

a. What decision would maximize expected profits?

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

a. Develop a decision table for this problem.

b. What is the best decision? 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.

a. Draw a decision table for this problem.

b. What do you recommend?