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 S S2 S Decision Alternative di dz 180 100 50 240 140 50 a. Choose the correct decision tree for this problem. () (ii) 180 180 $1 di si 240 240 s1 d di 100 100 13 di 52 140 140 52 d2 d2 50 50 53 di 53 50 50 $ 53 d2 (iii) (iv) 53 50 50 53 d2 ( ii) (iv) 180 100 s2 180 sl - di si 100 dh 52 50 53 50 53 240 si 140 140 s2 d2 S2 50 53 240 50 53 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