Problem 13-16 (Algorithmic) 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, di and d2, and two states of nature, si and s2. The payoff table showing proft is as follows: State of Nature Decision Alternative Si S2 di 300 200 d2 300 200 a. Choose the correct decision tree for this problem. (0) (11) Profit Payoff 300 Profit Payoff 300 di si di 200 300 F 300 200 di si S2 200 200 52 Market Research Market Research 300 300 di si si di 200 300 S2 300 200 si S2 200 200 300 300 di si si 200 300 d2 No Market Research No Market Research 300 200 du si S2 dh 200 200 (iv) Profit Payoff Profit Payoff 300 300 si si di di 200 -200 52 52 F 300 300 si Si 200 d 200 52 S2 No Market Research Market Research 300 300 si si di di 200 -200 52 300 300 si sl 200 200 52 52 300 300 si si di 200 200 52 52 Market Research No Market Research 300 300 S1 si 200 200 52 b. Using the following probabilities, what is the optimal decision strategy? PCF) = 0.64 P($11F) = 0.42 P(S1U) = 0.55 P(s) - 0.40 PU) = 0.36 P(S21F) = 0.58 P(S2|U) = 0.45 P(S2) = 0.60 Optimal decision strategy