Suppose that a decision maker faced with four decision alternatives and four states of nature develops the following profit payoff table:

State of nature

Decision Alternativs

12

7

5

9

10

8

11

8

5

9

12

7

7

8

8

12

a. If the decision maker knows nothing about the probabilities of the four states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?

b. Which approach do you prefer? Explain. Is establishing the most appropriate approach before analyzing the problem important for the decision maker?

c. Develop a decision tree if P(s1) = .15, P(s2) = .5, P(s3) = .25 and P(s4) = .10.

Question 3 (15 points) Suppose that a decision maker faced with four decision alternatives and four states of nature develops the following profit payoff table: State of nature Decision Alternativ 12 7 5 9 10 8 118 5 9127 788 12 a. If the decision maker knows nothing about the probabilities of the four states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches? b. Which approach do you prefer? Explain. Is establishing the most appropriate approach before analyzing the problem important for the decision maker? c. Develop a decision tree if (s) = 15, P(s) = -5, P(s) - 25 and P(s) = 10. Question 3 (15 points) Suppose that a decision maker faced with four decision alternatives and four states of nature develops the following profit payoff table: State of nature Decision Alternative 12 7 5 9 10 8 11 8 5 9 12 7 7 8 8 12 a. If the decision maker knows nothing about the probabilities of the four states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches? b. Which approach do you prefer? Explain. Is establishing the most appropriate approach before analyzing the problem important for the decision maker? c. Develop a decision tree if P(s) = .15, P(s) = .5, P(s) = .25 and P(s) = .10