QuestionA department store is about to order deluxe, standard, and economy… 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 net4?,2?,and1million? dollars, respectively, on sales of? deluxe, standard, and economy grade? models; if the economy is? down, the company will net-3?,0?,and4million? dollars, respectively, on sales of? deluxe, standard, and economy grade models. Complete parts A through D below.a) set up a payoff matrix for thus problemb)Find P* the optimal strategy for the row player, the department store. ______Find Q, the optimal strategy for the column player. the economy (fate) _______Find v, the value of the game _____c) how should the companys 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 the budget on deluxe, ____ of their budget on standard, and ____ of their budget on economyd) 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”?MathStatistics and Probability MATH 209
