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Question 2 (7.5 points): 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 S1 S2 S3 d1 150 180 130 d2 200 160 110 a. Construct a decision tree for this problem. (1 point) b. If the decision maker knows nothing about the probabilities of the three states of nature what is the recommended decision using the optimistic approach? (2.5 points) c. If the decision maker knows nothing about the probabilities of the three states of nature what is the recommended decision using the conservative approach? (2.5 points) d. If the decision maker knows nothing about the probabilities of the three states of nature what is the recommended decision using the minimax regret approach? (1.5 points)