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, d and d2, and two states of nature, s and s2. The payoff table showing proft is as follows: State of Nature Decision Alternative S S 100 d 300 d2 400 400 a. Choose the correct decision tree for this problem. (1) (ii) Profit Payoff 100 d d _300 F 400 400 100 Market Research d2 $1 52 $1 52 Profit Payoff 100 300 400 400 100 No Market Research F d2 $1 $2 $1 $2 (iii) No Market Research Market Research F U d1 d2 $1 $2. $1 Sa 52 $1 52 d d2 d d d d2 d .300 400 400 Profit Payoff 100 .300 400 400 100 .300 .400 (iv) Market Research Market Research F U d1 d d d2 d dh $2 $1 $2 $1 $2 $1 $2 $1 $2 $1 300 .400 -400 Profit Payoff 100 400 .300 .400 100 .400 .300 52 400 d2 100 d 300 d2 No Market Research 400 d $2 400 d2 b. Using the following probabilities, what is the optimal decision strategy? P(F) = 0.69 P(S1|U) = 0.70 P(S1|F) = 0.72 P(s2|F) = 0.28 P(U) = 0.31 P(S2|U) = 0.30 Optimal decision strategy: $1 P(S1) = 0.50 P(S2) = 0.50 No Market Research d2 d $2 $1 $2 $1 $2 400 100 400 .300 400