Problem 13-01 (Algorithmic) The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature: State of Nature Decision Alternative Si S2 Sz di 210 200 100 d2 300 170 50 a. Choose the correct decision tree for this problem. (1) (ii) 210 di S1 300 210 d2 S1 200 200 di d1 S2 100 S2 S3 170 300 d2 S1 100 170 d1 d2 S2 50 S3 S3 50 d2 (iii) (iv) 210 S1 210 200 S2 300 S1 di si di 200 S2 100 S3 170 s2 d2 170 2.- 100 S2 S3 O d2 S1 300 50 50 S3 S3 b. If the decision maker knows nothing about the probabilities of the three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches? Optimistic approach Conservative approach Minimax regret approach