a.
If perfect information is available, the highest payoff for each state of nature would be selected.
Therefore, the optimal decision strategy shall be as follows:
S1: d1 (300)
S2: d1 or d2 (175)
S3: d2 (100)
b.
Expected value with perfect information = Sum of ( Maximum payoff in State of nature x Probability of State of nature)
= ( 300 x 0.5) + ( 175 x 0.3) + ( 100 x 0.2)
= 150 + 52.5 + 20
= 222.5
c.
Expected value without perfect information = Maximum Expected monetary value (EMV)
EMV = Sum of ( Payoff in State of nature x Probability of State of nature)
Therefore,
EMV of d1 = ( 300 x 0.5) + ( 175 x 0.3) + ( 50 x 0.2) = 150 + 52.5 + 10 = 212.5
EMV of d2 = ( 200 x 0.5) + ( 175 x 0.3) + ( 100 x 0.2) = 100 + 52.5 + 20 = 172.5
Since d1 has the maximum EMV, the recommended decision would be to select d1.
Expected value of d1 = 212.5
d.
The expected value of Perfect information = Expected value with Perfect information - Maximum EMV
= 222.5 - 212.5
= 10
The following profit payoff table shows profit for a decision analysis problem with two decision alternatives...
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