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11 Pages

### Supplement 1

Course: MKTG 372, Spring 2012
School: Ole Miss
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Word Count: 614

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1 Supplement Solutions to Selected Problems Operational Decision-Making Tools: Decision Analysis S1-1. a. Minimin: South Korea 15.2 China 17.6 Taiwan 14.9 Poland 13.8 Mexico 12.5 minimum Select Mexico b. Minimax: South Korea 21.7 China 19.0 minimum Taiwan 19.2 Poland 22.5 Mexico 25.0 Select China c. Hurwicz ( = 0.40 ) : South Korea: 15.2 ( 0.40 ) + 21.7 ( 0.60 ) = 19.10 China: 17.6 ( 0.40 ) + 19.0 ( 0.60 ) =...

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1 Supplement Solutions to Selected Problems Operational Decision-Making Tools: Decision Analysis S1-1. a. Minimin: South Korea 15.2 China 17.6 Taiwan 14.9 Poland 13.8 Mexico 12.5 minimum Select Mexico b. Minimax: South Korea 21.7 China 19.0 minimum Taiwan 19.2 Poland 22.5 Mexico 25.0 Select China c. Hurwicz ( = 0.40 ) : South Korea: 15.2 ( 0.40 ) + 21.7 ( 0.60 ) = 19.10 China: 17.6 ( 0.40 ) + 19.0 ( 0.60 ) = 18.44 Taiwan: 14.9 ( 0.40 ) + 19.2 ( 0.60 ) = 17.48 minimum Poland: 13.8 ( 0.40 ) + 22.5 ( 0.60 ) = 19.02 Mexico: 12.5 ( 0.40 ) + 25.0 ( 0.60 ) = 20.0 Select Taiwan d. Equal likelihood: South Korea: 21.7 ( 0.33) + 19.1( 0.33) + 15.2 ( 0.33) = 18.48 China: 19.0 ( 0.33) + 18.5 ( 0.33) + 17.6 ( 0.33) = 18.18 Taiwan: 19.2 ( 0.33) + 17.1( 0.33) + 14.9 ( 0.33) = 16.90 minimum Poland: 22.5 ( 0.33) + 16.8 ( 0.33) + 13.8 ( 0.33) = 17.52 Mexico: 25.0 ( 0.33) + 21.2 ( 0.33) + 12.5 ( 0.33) = 19.37 Select Taiwan S1-2. EV ( South Korea ) = 21.7 ( .30 ) + 19.1(.40 ) + 15.2 (.30 ) = 18.71 EV ( China ) = 19.0 (.30 ) + 18.5 (.40 ) + 17.6 (.30 ) = 18.38 EV ( Taiwan ) = 19.2 ( .30 ) + 17.1(.40 ) + 14.9 (.30 ) = 17.07 minimum EV ( Poland ) = 22.5 (.30 ) + 16.8 (.40 ) + 13.8 (.30 ) = 17.61 EV ( Mexico ) = 25.0 (.30 ) + 21.2 (.40 ) + 12.5 (.30 ) = 19.73 Select Taiwan Expected value of perfect information = 19 (.30 ) + 16.8 (.40 ) + 12.5 (.30 ) = 16.17 EVPI = 16.17 17.07 = \$ 0.9 million The EVPI is the maximum amount the cost of the facility could be reduced (.9 million) if perfect information can be obtained. S1-3. a. Maximax criteria: Office building 4.5 maximum Parking lot 2.4 Warehouse 1.7 Shopping mall 3.6 Condominiums 3.2 Select office building b. Maximin criteria: Office building 0.5 Parking lot 1.5 maximum Warehouse 1.0 Shopping mall 0.7 Condominiums 0.6 Select parking lot c. Equal likelihood: Office building: 0.5 ( 0.33) + 1.7 ( 0.33) + 4.5 ( 0.33) = 2.21 maximum Parking lot: 1.5 ( 0.33) + 1.9 ( 0.33) + 2.4 ( 0.33) = 1.91 Warehouse: 1.7 ( 0.33) + 1.4 ( 0.33) + 1.0 ( 0.33) = 1.35 Shopping mall: 0.7 ( 0.33) + 2.4 ( 0.33) + 3.6 ( 0.33) = 2.21 maximum Condominiums: 3.2 ( 0.33) + 1.5 ( 0.33) + 0.6 ( 0.33) = 1.75 Select office building or shopping mall d. Hurwicz criteria ( = 0.3) : Office building: 4.5 ( 0.3) + 0.5 ( 0.7 ) = 1.70 Parking lot: 2.4 ( 0.3) + 1.5 ( 0.7 ) = 1.77 maximum Warehouse: 1.7 ( 0.3) + 1.0 ( 0.7 ) = 1.21 Shopping mall: 3.6 ( 0.3) + 0.7 ( 0.7 ) = 1.57 Condominiums: 3.2 ( 0.3) + 0.6 ( 0.7 ) = 1.38 Select parking lot S1-4. a) EV ( Office building ) = .5 ( .50 ) + 1.7 (.40 ) + 4.5 (.10 ) = 1.38 EV ( Parking lot ) = 1.5 (.50 ) + 1.9 (.40 ) + 2.4 (.10 ) = 1.75 EV ( Warehouse ) = 1.7 (.50 ) + 1.4 (.40 ) + 1.0 (.10 ) = 1.51 EV ( Shopping mall ) = 0.7 (.50 ) + 2.4 (.40 ) + 3.6 (.10 ) = 1.67 EV ( Condominiums ) = 3.2 (.50 ) + 1.5 (.40 ) + .06 (.10 ) = 2.26 maximum Select Condominium project b) EVPI = Expected value of perfect informationexpected value without perfect information = 3.012.26 = \$0.75 million S1-5. a. b. c. d. Maximax: Risk fund, maximax payoff = \$167, 000 Maximin: Savings bond maximin payoff = \$30, 000 Equal likelihood: Bond fund, maximum payoff = \$35, 000 Best decision, given probabilities: Bond fund, maximum payoff = \$35, 000 S1-7. a. Product Widget Expected Value 160, 000 ( 0.2 ) + 90,000 ( 0.5) 50, 000 ( 0.3) = \$62, 000 Hummer 70, 000 ( 0.2 ) + 40, 000 ( 0.5 ) + 20, 000 ( 0.3) = \$40, 000 Nimnot 45, 000 ( 0.2 ) + 35,000 ( 0.5 ) + 30, 000 ( 0.3) = \$35,500 The best option is to introduce the widget. b. EV given perfect information: 160, 000 ( 0.2 ) + 90, 000 ( 0.5) + 30, 000 ( 0.3) = \$86,000. EV without perfect information: Widget at \$62,000. Value of perfect information: \$86, 000 \$62, 000 = \$24, 000 The company would consider this a maximum; since perfect information is rare, it would probably pay less than \$24,000. c. Maximax: Introduce widget, maximax payoff = \$160, 000 Maximin: Introduce nimnot, maximin payoff = \$30, 000. Minimax regret: widget, Introduce Minimax regret = \$80, 000 Equal likelihood: Introduce widget, maximum payoff = \$66, 000 S1-9. Publication Decision Paperback Similar revision Major content revision Major physical revision Expected Value \$216,290 386,340 468,780 405,970 Best decision = major content revision Overall best decision appears to be a major content revision EVPI = (.23)(68,000) + (.46)(515,000) + (.31)(972,000) 468,780 = \$85,080 This is the maximum amount Wiley would pay an expert for additional information about the future competitive market. S1-15 Service Facility Child care center Swimming pool Lockers and showers Food court Spa Expected Value \$30,560 7,610 44,150 15,440 20,580 Best decision = Lockers and showers S1-16. a. Payoff table: Stock (lb) 20 21 22 23 24 20 0.10 20.00 18.50 17.00 15.50 14.00 21 0.20 20.00 21.00 19.50 18.00 16.50 Demand 22 0.30 20.00 21.00 22.00 20.50 19.00 23 0.30 20.00 21.00 22.00 23.00 21.50 24 0.10 20.00 21.00 22.00 23.00 24.00 EV ( 20 ) = \$20 EV ( 21) = 18.50 ( 0.1) + 21( 0.2 ) + 21( 0.3) + 21( 0.3) + 21( 0.1) = \$20.75 EV ( 22 ) = 17 ( 0.1) + 19.50 ( 0.2 ) + 22 ( 0.3) + 22 ( 0.3) + 22 ( 0.1) = \$21.00 EV ( 23) = 15.50 ( 0.1) + 18 ( 0.2 ) + 20.50 ( 0.3) + 23 ( 0.3) + 23 ( 0.1) = \$20.50 EV ( 24 ) = 14 ( 0.1) + 16.50 ( 0.2 ) + 19 ( 0.3) + 21.50 ( 0.3) + 24 ( 0.1) = \$19.25 Order 22 lb of apples for a profit of \$21.00. b. Maximax: Stock 24 lb for a maximax profit of \$24.00. Maximin: Stock 20 lb for a maximin profit of \$20.00. S1-17. a. Payoff table: Demand Stock (lb) (boxes) 25 26 27 28 29 30 25 0.10 50 49 48 47 46 45 26 0.15 50 52 51 50 49 48 27 0.30 50 52 54 53 52 51 28 0.20 50 52 54 56 55 54 29 0.15 50 52 54 56 58 57 EV ( 25 ) = 50 ( 0.1) + 50 ( 0.15 ) + 50 ( 0.3) + 50 ( 0.2 ) + 50 ( 0.15) + 50 ( 0.1) = \$50.00 EV ( 26 ) = 49 ( 0.1) + 52 ( 0.15 ) + 52 ( 0.3) + 52 ( 0.2 ) + 52 ( 0.15) + 52 ( 0.1) = \$51.70 EV ( 27 ) = 48 ( 0.1) + 51( 0.15 ) + 54 ( 0.3) + 54 ( 0.2 ) + 54 ( 0.15) + 54 ( 0.1) = \$52.95 EV ( 28 ) = 47 ( 0.1) + 50 ( 0.15) + 53 ( 0.3) + 56 ( 0.2 ) + 56 ( 0.15 ) + 56 ( 0.1) = \$53.30 30 0.10 50 52 54 56 58 60 EV ( 29 ) = 46 ( 0.1) + 49 ( 0.15 ) + 52 ( 0.3) + 55 ( 0.2 ) + 58 ( 0.15) + 58 ( 0.1) = \$53.05 EV ( 30 ) = 45 ( 0.1) + 48 ( 0.15) + 51( 0.3) + 54 ( 0.2 ) + 57 ( 0.15) + 60 ( 0.1) = \$52.35 Best decision: Stock 28 boxes, for a profit of \$53.30. b. Expected value under uncertainty: EV = 500 ( 0.10 ) + 52 ( 0.15) + 54 ( 0.30 ) + 56 ( 0.20 ) + 58 ( 0.15) + 60 ( 0.10 ) = \$54.90 EVPI = \$54.90 \$53.30 = \$1.60 S1-18. a) Stock 25, maximum of minimum payoffs = \$50 b) Stock 30, maximum of maximum payoffs = \$60 c) 25 : 50 (.4 ) + 50 (.6 ) = 50; 26 : 52 (.4 ) + 49 (.6 ) = 50.2; 27 : 54 (.4 ) + 48 (.6 ) = 50.4; 28 : 56 (.4 ) + 47 (.6 ) = 50.6; 29 : 58 (.4 ) + 46 (.6 ) = 50.8; 30 : 60 (.4 ) + 45 (.6 ) = 51; stock 30 boxes. d) Stock 28 or 29 boxes; minimum regret = \$4. S1-20. 1-28. EV ( snow shoveler ) = \$30 (.12 ) + 60 (.19 ) + 90 (.24 ) + 120 (.22 ) + 150 (.13) + 180 (.08 ) + 210 (.02 ) = \$101.10 The cost of the snow blower (\$575) is much more than the annual cost of the snow shoveler, thus on the basis of one year the snow shoveler should not be purchased. However, the snow blower could be used for an extended period of time such that after approximately 6 years the cost of the snow blower would be recouped. Thus, the decision hinges on weather or not the decision maker thinks 6 years is too long to wait to recoup the cost of the snow blower. S1-29. Since cost of installation (\$900,000) is greater than expected value of not installing (\$552,000), do not install an emergency power generator S1-30. Select strategy 3; Change oil regularly; EV = \$98.80 S1-31. Select Strategy 4; Change oil and sample; EV = \$716.40 S1-32. a. b. .98 9.2 x + 1.5 (1 x ) + (.02 )(1.5 ) = 3.810 .98 [ 7.7 x + 1.5] + .030 = 3.810 7.546 x + 1.47 + .030 = 3.810 7.546 x = 2.31 x = .306 probability of winning in overtime S1-33. S1-35. S1-36.
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