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 5, 3, and 2 million dollars, respectively, on sales of deluxe, standard, and economy grade models; if the economy is down, the company will net -3, 2, 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. Economy (fate) Up Down Deluxe 5 -3 Dept. Store Standard 3 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. (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? of their The company should spend of their budget on deluxe models, of their budget on standard models, and 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 0. (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.)
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 5, 3, and 2 million dollars, respectively, on sales of deluxe, standard, and economy grade models; if the economy is down, the company will net -3, 2, 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. Economy (fate) Up Down Deluxe 5 -3 Dept. Store Standard 3 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. (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? of their The company should spend of their budget on deluxe models, of their budget on standard models, and 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 0. (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.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text: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 5, 3, and 2 million dollars, respectively, on sales of deluxe, standard, and
economy grade models; if the economy is down, the company will net -3, 2, 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.
Economy (fate)
Up Down
Deluxe
5
-3
Dept. Store
Standard
3
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.
(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?
of their
The company should spend of their budget on deluxe models, of their budget on standard models, and
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
0.
(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.)
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