MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question
A company is considering a project which has three options. The payoffs are shown in the body of the table. In this instance, the payoffs are in terms of present values, which represent equivalent current dollar values of expected future income less costs. This is a convenient measure because it places all alternatives on a comparable basis. If a small facility is built, the payoff will be the same for all three possible states of nature. For a medium facility, low demand will have a present value of $7 million, whereas both moderate and high demand will have present values of $12 million. A large facility will have a loss of $4 million if demand is low, a present value of $2 million if demand is moderate, and a present value of $16 million if demand is high. The payoff table depicting revenues and is shown in the following table. payoffs (PV in millions) states of nature Low Option Moderate high Small 10 10 10 Medium 7 12 12 Large -4 2 16 (a) Which alternative should the manager choose under the maximax criterion? (b) Which option should the manager choose under the maximin criterion? (c) Which option should the manager choose under the LaPlace criterion? (d) Which option should the manager choose with the Hurwicz criterion with a = 0.2? ( (e) Using a minimax regret approach, what alternative should be chosen? (f) After reading about economic predictions, the manager has assigned the probability of low, moderate or low at 30%, 50% and 20% respectively. Using expected monetary values, what option should be chosen and what is the optimal expected value?
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Transcribed Image Text:A company is considering a project which has three options. The payoffs are shown in the body of the table. In this instance, the payoffs are in terms of present values, which represent equivalent current dollar values of expected future income less costs. This is a convenient measure because it places all alternatives on a comparable basis. If a small facility is built, the payoff will be the same for all three possible states of nature. For a medium facility, low demand will have a present value of $7 million, whereas both moderate and high demand will have present values of $12 million. A large facility will have a loss of $4 million if demand is low, a present value of $2 million if demand is moderate, and a present value of $16 million if demand is high. The payoff table depicting revenues and is shown in the following table. payoffs (PV in millions) states of nature Low Option Moderate high Small 10 10 10 Medium 7 12 12 Large -4 2 16 (a) Which alternative should the manager choose under the maximax criterion? (b) Which option should the manager choose under the maximin criterion? (c) Which option should the manager choose under the LaPlace criterion? (d) Which option should the manager choose with the Hurwicz criterion with a = 0.2? ( (e) Using a minimax regret approach, what alternative should be chosen? (f) After reading about economic predictions, the manager has assigned the probability of low, moderate or low at 30%, 50% and 20% respectively. Using expected monetary values, what option should be chosen and what is the optimal expected value?
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