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MGNT 4640 1. DECISION ANALYSIS HOMEWORK #2 The following payoff table provides the profits for each of four alternatives in each of three states of nature: States of Nature Alternatives A B C 1 120 60 -20 2 90 80 100 3 81 81 81 4 -50 90 110 ___________________________________ The probabilities for the states of nature are: P(A)=0.8, P(B) = 0.1, and P(C) = 0.1. (a) (b) (c) (d) 2. What decision would be made based on the optimistic criterion? What decision would be made based on the conservative criterion? What decision would be made based on the expected value criterion? Develop a regret table and use the regret criterion to find the decision. Teresa Granger is the manager of Chicago Cheese, which produces cheese spreads including E-Z Spread Cheese. The probability of various sales levels, in cases, is as follows: Sales in Cases 10 11 12 13 14 Probability 0.2 0.3 0.2 0.2 0.1 A case of E-Z Spread Cheese sells for $100 and has a cost of $75. Any cheese that is not sold by the end of the week is sold to a local food processor for $50. How many cases of E-Z Spread Cheese should Teresa produce each week to maximize profit? Use Expected Net Marginal Profit Analysis to answer this question. 3. During Christmas, Harry’s Hardware sells Christmas trees for a substantial profit. Unfortunately, any trees not sold at the end of the season are worthless. The table on the next page shows the demand for Christmas trees. MGNT 4640 DECISION ANALYSIS HOMEWORK #2 DEMAND FOR CHRISTMAS TREES PAGE 2 PROBABILITY 50 75 100 125 150 175 200 0.05 0.10 0.20 0.30 0.20 0.10 0.05 Harry sells trees for $15 each, but his cost is only $6. Solve each part below, first by using E(NMP) analysis. Then solve again, using pc. (a) (b) (c) How many trees should Harry stock at his hardware store? If the cost increased to $12 per tree and Harry continues to sell trees for $15 each, how many trees should Harry stock? Harry is thinking about increasing the price to $18 per tree. Assume that the cost per tree is $6. It is expected that the probability of selling 50, 75, 100, or 125 trees will be 0.25 each. Harry does not expect to sell more than 125 trees with this price increase. What supply level do you recommend? 4. In addition to selling Christmas trees during the Christmas holidays, Harry’s Hardware sells all of the ordinary hardware items. One of the most popular items is Great Glue HH, a glue made for Harry’s Hardware. The selling price is $2 per bottle, but unfortunately, the glue gets hard and unusable after one month. The cost of the glue is 75 cents. During the past several months, the mean sales of glue was 60 units, and the standard deviation was 7. How many bottles of glue should Harry’s Hardware stock? Assume that sales follow a normal distribution. 5. The marginal profit on Washington Reds, a brand of apples from the state of Washington, is $15 per case. The marginal loss is $35 per case. During the past year, the mean sales of Washington Reds was 45,000 cases, and the standard deviation was 4,450. How many cases of Washington Reds should be brought to market? Assume that sales follow a normal distribution. Answers 1. (a) Alternative 1; 120 (b) Alternative 3; 81 (c) Alternative 1; expected value = 100 (d) Alternative 2; least maximum regret = 30 2. Supply 12 cases 4. pc = .375; supply 62 bottles 3. (a) Supply 125 trees (b) Supply 100 (c) Supply 100 5. pc = .70; supply 42,686 cases