Calculator Problem 13-14 (Algorithmic) The following profit payoff table shows p

Question

Calculator Problem 13-14 (Algorithmic) The following profit payoff table shows profit for a decisian analysis problem with two decision alternatives and three states of nature State of Nature Decision Alternative S1 S2 S3 2DD 150 150 250 150 100 di d2 The probabilities for the states of nature are Pls1)-0.55, P(sz) = 0.25 and PS3)-0.2. a. What is the optimal decision strategy if perfect infarmation were available? S1 1 Sz : S5: d1 d2 b. What is th di or da value for the decision strategy developed in part (a)? If required, round your answer to one decimal place. c Using the expected value approach, what is the recommended decision without perfect information? What is its expected value? If required, round vour answer to one decimal place

Explanation / Answer

a) With perfect information, for a given state, decision that has the maximum payoff is selected. Therefore,

For s1, select d2   (payoff of d1 = 200, d2 = 250, so d2 is selected)

For s2, select d1 or d2   (as both have same payoff = 150)

For s3, select d1   (payoff of d1 = 150, d2 = 100, so d1 is selected)

b). Expected Value of decision strategy developed in part (a) = 250*0.55+150*0.25+150*0.2 = 205

c) Without perfect information,

Expected Value of d1 = 200*0.55+150*0.25+150*0.2 = 177.5

Expected Value of d2 = 250*0.55+150*0.25+100*0.2 = 195

Expected Value of d2 is higher. Therefore, recommended decision strategy is d2.

Expected Value = 195

d) Expected Value of Perfect Information = EVwPI - EVmax = 205 - 195 = 10

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