Chapter 20.3, Problem 8E

Consider a variation of the PDC decision tree shown in Figure 20.5. The company must first decide whether to undertake the market research study. If the market research study is conducted, the outcome will either be favourable (F) or unfavourable (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. Use the following probabilities. What is the optimal decision strategy?

$\begin{array}{l}P(F)=.56P(s_1|F)=.57P(s_1|U)=.18P(s_1)=.40\\ P(U)=.44P(s_2|F)=.43P(s_2|U)=.82P(s_2)=.60\end{array}$

FIGURE 20.5 THE PDC DECISION TREE WITH BRANCH PROBABILITIES