A manager has learned that annual profits from four alternatives being considere
ID: 426798 • Letter: A
Question
A manager has learned that annual profits from four alternatives being considered for solving a capacity problem are projected to be $15,000 for A, $30,000 for B, $45,000 for C, and $60,000 for D if state of nature 1 occurs; and $60,000 for A, $80,000 for B, $90,000 for C, and $35,000 for D if state of nature 2 occurs. (A) Assuming maximax is used, what alternative would be chosen? (B) Assuming maximin is used, what alternative would be chosen? (C) Assuming Laplace is used, what alternative would be chosen? (D) If the probability of Nature 1 is.40 and the probability of Nature 2 is 0.6, which alternative should be chosen?Explanation / Answer
(A)
Max payoff of A = MAX(15000, 60000) = 60000
Max payoff of B = MAX(30000, 80000) = 80000
Max payoff of C = MAX(45000, 90000) = 90000
Max payoff of D = MAX(60000, 35000) = 60000
Maximum of the Max payoff is 90000, corresponding to alternative C.
Therefore, according to Maximax, alternative C would be chosen.
(B)
Min payoff of A = MIN(15000, 60000) = 15000
Min payoff of B = MIN(30000, 80000) = 30000
Min payoff of C = MIN(45000, 90000) = 45000
Min payoff of D = MIN(60000, 35000) = 35000
Maximum of the Min payoff is 45000, corresponding to alternative C.
Therefore, according to Maximin, alternative C would be chosen.
(C)
Average payoff of A = AVERAGE(15000, 60000) = 37500
Average payoff of B = AVERAGE(30000, 80000) = 55000
Average payoff of C = AVERAGE(45000, 90000) = 67500
Average payoff of D = AVERAGE(60000, 35000) = 47500
Maximum of the Average payoffs is 67500, corresponding to alternative C.
Therefore, according to Laplace criterion, alternative C would be chosen.
(D) Expected Monetary Value (EMV) approach
EMV of A = 15000*0.4+60000*0.6 = 42000
EMV of B = 30000*0.4+80000*0.6 = 60000
EMV of C = 45000*0.4+90000*0.6 = 72000
EMV of D = 60000*0.4+35000*0.6 = 45000
Maximum of the Average payoffs is 72000, corresponding to alternative C.
Therefore, according to EMV approach, alternative C would be chosen.
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