Consider the decision tree in Figure 18.9 and the situation described in Exercise 18.34. 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: €œfavorable€ (indicating that demand will be high) or €œunfavorable€ (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:

Figure 18.9

For instance, P(favorable | high) = .9 and P(unfavorable | low) = .8. Given the prior probabilities and payoffs in Figure 18.9, 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.

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True Demand High .9 .1 Study Outcome Favorable Unfavorable Low .2 .8 $40 Low demand (.4) Do nothing Overtime Horo $40 High demand (.6) -$50 Build small Expand $55 -$10 Do nothing Build large Reduce prices $50 Low demand (.4) High demand (.6) $70