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Question 2 (45 points). A manager is trying to decide whether to build a small, medium, or large facility. Demand can be low, average, or high, with the estimated probabilities being 0.25, 0.40, and 0.35, respectively. A small facility is expected to earn an after-tax net present value of just $18,000 if demand is low. If demand is average, the small facility is expected to earn $75,000; it can be increased to medium size to carn a net present value of $60,000. If demand is high, the small facility is expected to earn $75,000 and can be expanded to medium size to earn $60,000 or to large size to earn $125,000. A medium-sized facility is expected to lose an estimated $25,000 if demand is low and earn $140,000 if demand is average. If demand is high, the medium-sized facility is expected to earn a net present value of $150,000; it can be expanded to a large size for a net payoff of $145,000. If a large facility is built and demand is high, earnings are expected to be $220,000. If demand is average for the large facility, the present value is expected to be $125,000; if demand is low, the facility is expected to lost $60,000. Which alternative is best, according to each of the following decision criterion? a) Maximin I b) Maximax c) Minimax regret If a small facility is built and demand is average, then NPV of small facility is higher, so, it should not be upgraded to medium. Similarly, if demand is high, then small facility should be upgraded to large facility to earn NPV of $ 125,000 Medium facility should not be upgraded to large facility, if demand is high, because NPV of medium facility is higher. Taking into account these considerations, resulting Payoff table and regret table are following: B D E G F Demand Average 75000 140000 125000 0.4 Low 18000 -25000 -60000 0.25 1 High 125000 150000 220000 0.35 Max 125000 150000 220000 A 1 Payoff Table 2 3 After-tax NPV Build Small Facility 5 Build Medium Facility 6 Build Large Facility 7 Probability 8 9 10 Regret Table 11 After-tax NPV 12 Build Small Facility 13 Build Medium Facility 14 Build Large Facility 15 16 Min 18000 -25000 -60000 Low 0 43000 78000 Average 65000 0 15000 High 95000 70000 0 Max 95000 70000 78000 a) Maximin- Maximum of the minimum payoff is 18,000 associated with Small facility. Therefore, the best alternative is Build Small Facility b) Maximax - Maximum of the maximum payoff is 220,000 associated with Large facility. Therefore, the best alternative is Build Large Facility c) Minimax regret Minimum of the maximum regret is 70,000 associated with Medium facility, Therefore, the best alternative is Build Medium Facility In the second problem, you have to make check the small facility payoff in high demand again. Note that changing that payoff will make a change in the regret table as well