A buyer for a large department store chain must place orders with an athletic shoe manufacturer 6 months prior to the time the shoes will be sold in the department stores. In particular, the buyer must decide on November 1 how many pairs of the manufacturer’s newest model of tennis shoes to order for sale during the upcoming summer season. Assume that each pair of this new brand of tennis shoes costs the department store chain $45. Furthermore, assume that each pair of these shoes can then be sold to the chain’s customers for $70. Any shoes remaining unsold at the end of the summer season will be sold in a closeout sale next fall for $35 per pair. The probability distribution of consumer demand for these tennis shoes (in hundreds of pairs) during the upcoming summer season has been assessed by market research specialists and is provided in the file P10_40.xlsx. Finally, assume that the department store chain must purchase these tennis shoes from the manufacturer in lots of 100 pairs.

a. Create a payoff table that specifies the contribution to profit (in dollars) from the sale of the tennis shoes by this department store chain for each possible purchase decision (in hundreds of pairs) and each outcome with respect to consumer demand.

b. Use PrecisionTree to identify the strategy that maximizes the department store chain’s expected profit earned by purchasing and subsequently selling pairs of the new tennis shoes.

c. Perform a sensitivity analysis on the optimal decision and summarize your findings. In response to which model inputs is the expected earnings value most sensitive?