Consider the payoff table below. Assume that the probabilities of the states of nature are as follows:

P(s1) = 0.4 P(s2) = 0.3 P(s3) = 0.3

s1 s2 s3

Alternative 1: 5 7 8

Alternative 2: 6 6 6

Alternative 3: 3 9 1

A) Find the alternative that maximizes the expected net dollar return.

B) Find the alternative that minimizes the expected regret.

C) Suppose that P(s1) and P(s2) are not known, but P(s3) is estimated to be 0.1. Plot expected net dollar return versus P(s2) for the three alternatives in the same graph, and find the range for P(s2) for which each alternative is optimal.

D) In the same scenario as part (c), plot expected regret versus P(s2) for the three alternatives in the same graph, and find the range for P(s2) for which each alternative is optimal.

E) How are the plots in parts (c) and (d) related?