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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?
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?
Expert Answer
| 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
