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Unformatted text preview: 1 AB103 – Statistical and Quantitative Methods Solutions  Tutorial 4 Chapters 6 Anderson, Sweeney, Williams, and Martin (ASWM) 6.4 (page 326) a. The decision is to choose the best lease option; there are three alternatives. The chance event is the number of miles Amy will drive per year. There are three possible outcomes. b. The payoff table for Amy's problem is shown below. To illustrate how the payoffs were computed, we show how to compute the total cost of the Forno Saab lease assuming Amy drives 15,000 miles per year. Total Cost = (Total Monthly Charges) + (Total Additional Mileage Cost) = 36($299) + $0.15(45,000  36,000) = $10,764 + $1350 = $12,114 c. Optimistic Approach: Forno Saab ($10,764) Conservative Approach: Hopkins Automotive ($11,700) Opportunity Loss or Regret Table 2 d. EV (Forno Saab) = 0.5($10,764) + 0.4($12,114) + 0.1($13,464) = $11,574 EV (Midtown Motors) = 0.5($11,160) + 0.4($11,160) + 0.1($12,960) = $11,340 EV (Hopkins Automotive) = 0.5($11,700) + 0.4($11,700) + 0.1($11,700) = $11,700 Best Decision: Midtown Motors e. f. EV (Forno Saab) = 0.3($10,764) + 0.4($12,114) + 0.3($13,464) = $12,114 EV (Midtown Motors) = 0.3($11,160) + 0.4($11,160) + 0.3($12,960) = $11,700 EV (Hopkins Automotive) = 0.3($11,700) + 0.4($11,700) + 0.3($11,700) = $11,700 Best Decision: Midtown Motors or Hopkins Automotive With these probabilities, Amy would be indifferent between the Midtown Motors and Hopkins Automotive leases. However, if the probability of driving 18,000 miles per year goes up any further, the Hopkins Automotive lease will be the best. 3 10. a. b. EV(node 2) = 0.2(1000) + 0.5(700) + 0.3(300) = 640 EV(node 4) = 0.3(800) + 0.4(400) + 0.3(200) = 460 EV(node 5) = 0.5(1600) + 0.3(800) + 0.2(400) = 1120 EV(node 3) = 0.6EV(node 4) + 0.4EV(node 5) = 0.6(460) + 0.4(1120) = 724 Space Pirates is recommended. Expected value of $724,000 is $84,000 better than Battle Pacific. c. Risk Profile for Space Pirates Outcome: 1600 (0.4)(0.5) = 0.20 800 (0.6)(0.3) + (0.4)(0.3) = 0.30 400 (0.6)(0.4) + (0.4)(0.2) = 0.32 200 (0.6)(0.3) = 0.18 1 5 400 800 1600 200 400 800 300 700 1000 High Medium Low 0.3 0.4 0.3 High Medium Low 0.5 0.3 0.2 High Medium Low 0.2 0.5 0.3 4 2 3 With Competition 0.6 Without Competition 0.4 Battle Pacific Space Pirates 4 d. Let p = probability of competition p = 0 EV(node 5) = 1120 p = 1 EV(node 4) = 460 1120  p (1120  460) = 640 660 p = 480 p = 480/660 = 0.7273 The probability of competition would have to be greater than 0.7273 before we would change to the Battle Pacific video game. 13. a. The decision is to choose what type of grapes to plant, the chance event is demand for the wine and the consequence is the expected annual profit contribution. There are three decision alternatives (Chardonnay, Riesling and both). There are four chance outcomes: (W,W); (W,S); (S,W); and (S,S). For instance, (W,S) denotes the outcomes corresponding to weak demand for Chardonnay and strong demand for Riesling....
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This note was uploaded on 03/21/2010 for the course BIZ ab103 taught by Professor Woo during the Spring '10 term at Nanzan.
 Spring '10
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