Chapter 10.4, Problem 11E

Headphone sales. A department store chain is about to order deluxe, standard, and discount headphones for next year’s inventory. The state of the nation’s economy (fate) during the year will be an important factor on sales for that year. Records over the past $5$ years indicate that if the economy is up, the company will net $3$, $1$, and $0$ million dollars, respectively, on sales of deluxe, standard, and discount models. If the economy is down, the company will net $-1,1$, and $3$ million dollars, respectively, on sales of deluxe, standard, and discount models.

(A) Set up a payoff matrix for this problem.

(B) Find optimal strategies for both the company and fate (the economy). What is the value of the game?

(C) How should the company’s budget be allocated to each grade of headphone to maximize the company’s return respective of what the economy does the following year?