13. A department store is about to order deluxe, standard, and economy grade DVD players for next year's inventory. The state of the nation's economy (fate) during the year will be a factor on sales for that year. Records over the past 5 years show that if the economy is up, the store will net 3, 2, and 1 million dollars, respectively, on sales of deluxe, standard, and economy grade models; if the economy is down, the company will net -2, -1, and 5 million dollars, respectively, on sales of deluxe, standard, and economy grade models. Complete parts A through D below. (A) Set up a payoff matrix for this problem. Up Economy (fate) Down Dept. Store Deluxe Standard Economy (B) Find optimal strategies for both the company and fate (the economy). What is the value of the game? Find P*, the optimal strategy for the row player, the department store. P*= (Simplify your answer.) Find Q", the optimal strategy for the column player, the economy (fate). Q' = (Simplify your answer.) Find v, the value of the game. v= (Simplify your answer.) (C) How should the company's budget be allocated to each grade of DVD player to maximize their return irrespective of what the economy does the following year? The company should spend of their budget on deluxe models, of their budget on standard models, and of their budget on economy models. (Simplify your answers.) (D) What is the expected value of the game to the company if it orders only deluxe DVD players and fate plays the strategy "Down"? If the company plays its optimal strategy and fate plays the strategy "Down"? The expected value of the game to the company if it orders only deluxe DVD players and fate plays the strategy "Down" is (Simplify your answer.) The expected value of the game to the company if it plays its optimal strategy and fate plays the strategy "Down" is (Simplify your answer.)