Suppose that a decision maker faced with three decision alternatives and three states of nature develops the following profit payoff table (profits in $s). States of Nature Decision Alternative s1 s2 s3 d1 650 640 600 d2 900 600 300 d3 800 630 400 a. a. Please draw a decision tree to illustrate the decision problem. 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? (details are required as the example in lecture notes)? c. What is the recommended decision using the conservative approach (details are required as the example in lecture notes)? 2 d. What is the recommended decision using minimax regret approaches (A regret table is required and details are required as the example in lecture notes)? e. Suppose the decision maker obtained the probability assessments P(s1) = 0.2, P(s2) = 0.5, P(s3) = 0.3. Use the expected value approach to determine the optimal decision.