Mountain Ski Sports, a chain of ski equipment shops in Colorado, purchases skis from a manufacturer each summer for the coming winter season. The most popular intermediate model costs $150 and sells for $260. Any skis left over at the end of the winter are sold at the store's half price sale (for $130). Sales over the years are quite stable. Gathering data from all its stores, Mountain Ski Sports developed the following probability distribution for demand:
Demand Probability
150 0.05
175 0.15
200 0.40
225 0.30
250 0.10
The manufacturer will take orders only for multiples of 20, so Mountain Ski is considering the following order sizes: 160, 180, 200, 220, and 240.
a. Construct a payoff table for Mountain Ski's decision problem of how many pairs of skis to order. What is the best decision from an expected value basis?
b. Find the expected value of perfect information.
c. What is the expected demand? Is the optimal order quantity equal to the expected demand? Why?