Problem:
An appliance dealer must decide how many (if any) new microwave ovens to order for next month. The ovens cost $220 and sell for $300. Because the oven company is coming out with a new product line in two months, any ovens not sold next month will have to be sold at the dealer's half price clearance sale. Additionally, the appliance dealer feels he suffers a loss of $25 for every oven demanded when he is out of stock. On the basis of past months' sales data, the dealer estimates the probabilities of monthly demand (D) for 0, 1, 2, or 3 ovens to be .3, .4, .2, and .1, respectively.
The dealer is considering conducting a telephone survey on the customers' attitudes towards microwave ovens. The results of the survey will either be favorable (F), unfavorable (U) or no opinion (N). The dealer's probability estimates for the survey results based on the number of units demanded are:
P(FID = 0) = .1 P(FID = 2) = .3 P(UID = 0) = .8 P(UID = 2) = .1
P(FID = 1) = .2 P(FID = 3) = .9 P(UID = 1) = .3 P(UID = 3) = .1
Required:
Question 1) What is the dealer's optimal decision without conducting the survey?
Question 2) What is the EVPI?
Question 3) Based on the survey results what is the optimal decision strategy for the dealer?
Question 4) What is the maximum amount he should pay for this survey?
Solve the given numerical problem and illustrate step by step calculation.