# B yes allen should pay 110004 90004 90002 900 80 3 10

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b. Yes, Allen should pay [1,100(0.4) + 900(0.4) + 900(0.2)] – 900 = \$80. 3-10
3-24. a. Opportunity loss table Strong Fair Poor Max. Market Market Market Regret Large 0 19,000 310,000 310,000 Medium 250,000 0 100,000 250,000 Small 350,000 29,000 32,000 350,000 None 550,000 129,000 0 550,000 b. Minimax regret decision is to build medium. 3-25. a. Stock Demand (Cases) (Cases) 11 12 13 EMV 11 385 385 385 385 12 329 420 420 379.05 13 273 364 455 341.25 Probabilities 0.45 0.35 0.20 b. Stock 11 cases. c. If no loss is involved in excess stock, the recommended course of action is to stock 13 cases and to replenish stock to this level each week. This follows from the following decision table. Stock Demand (Cases) (Cases) 11 12 13 EMV 11 385 385 385 385 12 385 420 420 404.25 13 385 420 455 411.25 3-11
3-26. Manufacture (Cases) Demand (Cases) 6 7 8 9 EMV 6 300 300 300 300 300 7 255 350 350 350 340.5 8 210 305 400 400 352.5 9 165 260 355 450 317 Probabilities 0.1 0.3 0.5 0.1 John should manufacture 8 cases of cheese spread. 3-27. Cost of produced case = \$5. Cost of purchased case = \$16. Selling price = \$15. Money recovered from each unsold case = \$3. Supply Demand(Cases) (Cases) 100 200 300 EMV 100 100(15) –100(5) = 1000 200(15) – 100(5) –100(16) = 900 300(15) – 100(5) –200(16) = 800 900 200 100(15) + 100(3) –200(5) = 800 200(15) – 200(5) = 2000 300(15) – 200(5) –100(16) = 1900 1610 300 100(15) + 200(3) – 300(5) = 600 200(15) + 100(3) –300(5) = 1800 300(15) – 300(5) = 3000 1800 Prob. 0.3 0.4 0.3 b. Produce 300 cases each day. 3-12
3-28. a. The table presented is a decision table. The basis for the decisions in the following questions is shown in the table. The values in the table are in 1,000s. Decision M ARKET M AXIMAX M AXIMIN E QUALLY L IKELY C RIT . OF R EALISM Alternatives Good Fair Poor Row Max. Row Min. Row Ave. Weighted Ave. Small 50 20 –10 50 –10 20 38 Medium 80 30 –20 80 –20 30 60 Large 100 30 –40 100 –40 30 72 Very Large 300 25 –160 300 –160 55 208 b. Maximax decision: Very large station. c. Maximin decision: Small station. d. Equally likely decision: Very large station. e. Criterion of realism decision: Very large station. f. Opportunity loss table (values in the table are in 1,000s): M ARKET M INIMAX Decision Good Fair Poor Row Alternatives Market Market Market Maximu m Small 250 10 0 250 Medium 220 0 10 220 Large 200 0 30 200 Very Large 0 5 150 150 3-13
3-29 . Note this problem is based on costs, so the minimum values are the best. a. For a 3-year lease, there are 36 months of payments. Option 1 total monthly payments: 36(\$330) = \$11,880 Option 2 total monthly payments: 36(\$380) = \$13,680 Option 3 total monthly payments: 36(\$430) = \$15,480 Excess mileage costs based on 36,000 mileage allowance for Option 1, 45,000 for Option 2, and 54,000 for option 3. Option 1 excess mileage cost if 45,000 miles are driven = (45000 – 36000)(0.35) = 3150 Option 1 excess mileage cost if 54,000 miles are driven = (54000 – 36000)(0.35) = 6300 Option 2 excess mileage cost if 54,000 miles are driven = (54000 – 45000)(0.25) = 2250 The total cost for each option in each state of nature is obtained by adding the total monthly pay- ment cost to the excess mileage cost. Total cost table Lease option 36000 miles driven 45000 miles driven 54000 miles driven Option 1 11,880 15030 18180 Option 2 13,680 13680 15930 Option 3 15,480 15480 15480 b. Optimistic decision: Option 1 because the best (minimum) payoff (cost) for this is 11,800 which is better (lower) than the best payoff for each of the others.