# Answered! Given the attached payoff table, determine the expected value of the best management decision, then the best…

Given the attached payoff table, determine the expected value of the best management decision, then the best outcome with perfect information, and the max value of the information.

 Demand 1 Demand 2 Demand 3 Alternative A 100 75 50 Alternative B 50 125 -25 Alternative C -25 75 200 Probability 40% 55% 5%

1. Rounded to the nearest penny, what is the expected value of the best management decision?

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2. Rounded to the nearest penny, what is the expected outcome if the demand can be predicted with 100% accuracy?

3. Rounded to the nearest penny, what is the maximum value of this perfect information?

With the given probabilities and the payoff matrix, we can find the expected monetary values as following:
 Demand 1 Demand 2 Demand 3 EMV Alternative A 100 75 50 83.75 Alternative B 50 125 -25 87.50 Alternative C -25 75 200 41.25 Probability 40% 55% 5%

Sample Calculation: For Alternative A, EMV = 100*40% + 75*55% + 50*5% = 83.75

It is clear from the above table that the max.EMV is 87.50 and this happens to be the case of Alternative B.

So, the expected value of best management decision = max.EMV = 87.50 —————-1

With 100% accurate prediction,

For predicted state of nature: Demand 1, our selection of best payoff = 100 (Alternative A)

For predicted state of nature: Demand 2, our selection of best payoff = 125 (Alternative B)

For predicted state of nature: Demand 3, our selection of best payoff = 200 (Alternative C)

So, the Expected outcome with perfect information = 100*40% + 125*55% + 200*5% = 118.75 —-2

So, the value of this perfect information

= Expected outcome with perfect information – max.EMV = 118.75 – 87.50 = 31.25 ———–3