Consider the decision tree in Figure 19.9 and the situation described in Exercise 19.34. Suppose that a marketing research study can be done to obtain more information about whether demand will be high or low. The marketing research study will result in one of two outcomes: "favorable" (indicating that demand will be high) or "unfavorable" (indicating that demand will be low). The accuracy of marketing research studies like the one to be carried out can be expressed by the conditional probabilities in the following table:

For instance, P(favorable | high) = .9 and P(unfavorable | low) = .8. Given the prior probabilities and payoffs in Figure 19.9, do the following:
a. Carry out a posterior analysis. Find the best alternative (build small or build large) for each possible study result (favorable or unfavorable), and find the associated expected payoffs.
b. Carry out a preposterior analysis. Determine the maximum amount that should be paid for the marketing research study.

True Demand High Study Outcome Favorable Unfavorable Low .2 .8