A company estimates that its future demand is high (HD), moderate (MD) and low (LD) with the probabilities of 0.25, 0.45 and 0.30, respectively. The payoff table is given as

Now the company considers hiring a marketing research firm to do a study to determine whether the outlook for the future demand is positive, negative, or neutral. The cost of the study is $5K. The firm has previously done 100 studies for the company:

The additional alternatives were entered partially as follows into TreePlan. Use Bayes Theorem to calculate the necessary probabilities (to three decimal places, e.g. 0.3542...=0.354).

The expected monetary value EMV at the event node (green) located at the end of "Build Small" branch shown on the decision tree picture:

Question 12 options:

	Greater than or equal to 42K and less than 47K
	Greater than or equal to 52K and less than 57K
	Greater than or equal to 38K and less than 42K
	Greater than or equal to 57K
	Less than 38K

\begin{tabular}{|l|l|l|l|} \hline \multirow{2}{*}{ Alternatives } & \multicolumn{2}{|l|}{ State of Nature } \\ \cline { 2 - 4 } & HD & MD & LD \\ \hline Build Large Plant & $250,000 & $140,000 & $120,000 \\ \hline Build Small Plant & $120,000 & $70,000 & $40,000 \\ \hline Outsource & $50,000 & $20,000 & $10,000 \\ \hline Do Nothing & $0 & $0 & $0 \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|l|} \hline \multicolumn{2}{l|}{} & \multicolumn{2}{l|}{ Study information } & Total \\ \cline { 2 - 4 } & Positive & Negative & Neutral & \\ \hline HD & 30 & 2 & 3 & 35 \\ \hline MD & 9 & 7 & 10 & 26 \\ \hline LD & 3 & 32 & 4 & 39 \\ \hline \hline \end{tabular}