The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature.DecisionAlternatived₁d₂States of Nature515₂ 53260 110 35110 110 85The probabilities for the states of nature are P(S₁) = 0.65, P(S₂) = 0.15, and P(s) = 0.20.(a) What is the optimal decision strategy if perfect information were available?If s, then?;If s₂ then 2✓; If s₂ then ?(b) What is the expected value for the decision strategy developed in part (a)?(c) Using the expected value approach, what is the recommended decision without perfect information? What is its expected value?The recommended decision without perfect information is ?EV =(d) What is the expected value of perfect information?EVPI =

Decision AlternativesStates of NatureS1S2S3d126011035d211011085Probabilities for the states of nature-P(S1) = 0.65P(S2) = 0.15P(S3) = 0.20Part (A):If perfect information were available:The optimal strategy -If S1 then d1 (because d1 has higher payoff i.e. 260>110)If S2 then d1 or d2 (because both payoffs are equal 110=110)If S3 then d2 (because d2 has higher payoff i.e. 85>35)Part (B):Decision strategy developed in Part (A)-S1 = 260 and P(S1) = 0.65S2 = 110 and P(S2) = 0.15S3 = 85 and P(S3) = 0.20Thus, the Expected Value = 260*0.65 + 110*0.15 + 85*0.20 = 202.5Part (C):Expected value for d1 = 260*0.65 + 110*0.15 + 35*0.20 = 192.5Expected value for d2 = 110*0.65 + 110*0.15 + 85*0.20 = 105Here, the EV(d1) is higher than the EV(d2)Thus, the recommended decision without perfect information is for d1 with an EV of 192.5Part (D):The expected value of perfect information (EVPI) = EVwithPI - EVwithoutPI = 202.5 - 192.5 = 10Therefore-Part (A):The optimal strategy is -If S1 then d1If S2 then d1 or d2If S3 then d2Part (B):EV = 202.5Part (C):The recommended decision without perfect information is d1EV = 192.5Part (D):EVPI = 10