A firm is considering the marketing of a new product. For convenience, suppose that the events of interest are simply 1="new product is a success" and 2="new product is a failure." The prior probabilities are P(1)=0.3 and P(2)=0.7. If the product is marketed and is a failure, the firm suffers a loss of $300,000. If the product is not marketed and it would be a success, the firm suffers an opportunity loss of $500,000. The firm is considering two separate surveys, A and B, and the results from each survey can be classified as favorable, neutral, and unfavorable. The conditional probabilities for survey A are

P(favorable | 1) = 0.6, P(neural | 1) = 0.3, P(unfavorable | 1) = 0.1,

P(favorable | 2) = 0.1, P(neural | 2) = 0.2, P(unfavorable | 2) = 0.7.

The conditional probabilities for survey B are

P(favorable | 1) = 0.8, P(neural | 1) = 0.1, P(unfavorable | 1) = 0.1,

P(favorable | 2) = 0.1, P(neural | 2) = 0.4, P(unfavorable | 2) = 0.5.

Survey A costs $20,000 and survey B costs $30,000.

(a) Find the expected value of perfect information about .

(b) Find the expected net gain from survey A.

(c) Find the expected net gain from survey B.

(d) Suppose that the firm has a choice. It can use no survey, survey A, or survey B, but not both surveys. What is the optimal course of action?