please help me answer the following in a step by step process

please use 6 decimal places while computing and 4 decimal places in the final answer

3. (a-b). The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The state-of-nature probabilities are P(s,) = 0.35, P(s2) = 0.35, and P($3) = 0.30. The following payoff table shows the projected profit (in thousands of dollars): State of Nature Low Demand Medium Demand High Demand Decision Alternative $2 Manufacture, -20 40 100 Purchase. d2 10 45 70 a. Use expected value to recommend a decision. b. Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand.3. (c-f). The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. State of Nature Low Demand Medium Demand High Demand Decision Alternative $1 Manufacture, d -20 40 100 Purchase. da 10 45 70 The relevant conditional probabilities are as follows: P(F S, ) = 0.10 P(U | $1) = 0.90 P(F | $2) = 0.40 P(U | 52) = 0.60 P(F $3) = 0.60 P(U $3) - 0.40 C. A test market study of the potential demand for the product is expected to report either a favorable (F) or unfavorable (U] condition. i. Compute the Posterior Probabilities by completing the table Ti. What is the probability that the market research report will be favorable? III. What is the probability that the market research report will be unfavorable? iv. Draw the decision tree leading to market study/ prediction of favorable condition. V. Draw the decision tree leading to market study/ prediction of unfavorable condition. vi. Draw the decision tree incorporating the 2 conditions. d. What is Gorman's optimal decision strategy? e. What is the expected value of the market research information? f. What is the efficiency of the information