Consider a variation of the PDC decision tree shown in Figure 4.9. The company must first decide whether to undertake the market research study. If the market research study is conducted, the outcome will either be favorable (F) or unfavorable (U). Assume there are only two decision alternatives, d1 and d2, and two states of nature, s1 and s2. The payoff table showing profit is as follows:

a. Show the decision tree.
b. Using the following probabilities, what is the optimal decision strategy?
P(F) = 0.56 .......... P(s1|F) = 0.57 ...... P(s1|U) = 0.18 .............. P(s1) = 0.40
P(U) = 0.44 .........P(s2|F) = 0.43 ...... P(s2|U) = 0.82 .............. P(s2) = 0.60

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State of Nature Decision Alternative 100 400 300 200 d2