1. (50 points) (This problem is similar to problem 4.0.2 in notes). Suppose that a decision maker faced with four decision alternatives and four states of nature develops the following profit payoff table: State of Nature S1 S2 S3 $4 di 11 Decision Alternative 13 10 11 d2 9 10 12 10 d3 12 10 13 9 | da 8 9 14 13 1. If the decision maker knows nothing about the probabilities of the fours states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches? 2. Which approach do you prefer? Explain. Is establishing the most appropriate approach before analyzing the problem important for the decision maker? Explain. 3. Assume that the payoff table provides cost rather than profit payoffs. What is the recommended decision using the optimistic, conservative, and minimax regret approaches