Consider the following payoff table that represents the profits earned for each alternative (A, B, and C) under the states of nature $1, S2, and S3. SI $2 $3 Alternative A $60 $145 $120 Alternative B $75 $125 $110 Alternative C $95 $85 $130 a) Using each of the below criterion what would be the alternative selected and highest expected payoff in $ value? 1) Optimistic Approach 2) Pessimistic Approach 3) Realism (Hurwicz criterion) with an alpha value of 0.7 4) Laplace 5) Minmax regret Approach b) Suppose the likelihood of occurrence of the three state of natures are: S1 = 0.2; $2 = 0.3; & S3 = 0.5. 1) What is the EMV of each alternative and which one to select? 2) What is the EVwPI and EVPI? 3) Construct the EOL table. 4) What is the EOL for each alternative and which one to select? 5) Verify that the minimum EOL is equal to EVPI c) Suppose the payoff matrix is in fact a cost matrix. Redo parts (a) & (b) above