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A tour agency organizes standard and luxury tours for the following year. Once the agency has committed to these tours, the schedule cannot be changed. The state of the economy during the following year has a direct effect on tour sales. From the past records the agency has established the following payoff matrix (in millions of dollars). Down Economy (Fate) No change Up Standard 1 Luxury 4 0 2 3 Complete parts (A) through (C) below. (A) • Determine the Matrix M, the game matrix free of recessive rows and columns. M= • Find P*, the optimal strategy for the agency. P*= • Find Q*, the optimal strategy for the economy (fate). Q*= . Find v, the value of the game. v=$ (B) What proportion of each type of tour should be arranged for in advance in order for the agency to maximize its return irrespective of what the economy does the following year? (C) • • Standard: Luxury: What is the expected value of the game to the agency if they organize only luxury tours and fate plays strategy "down"? • The expected value is $ What is the expected value of the game if the agency plays its optimal strategy and fate plays the strategy "no change"? The expected value is $

A tour agency organizes standard and luxury tours for the following year. Once the agency has committed to these tours, the schedule cannot be changed. The state of the economy during the following year has a direct effect on tour sales. From the past records the agency has established the following payoff matrix (in millions of dollars). Down Economy (Fate) No change Up Standard 1 Luxury 4 0 2 3 Complete parts (A) through (C) below. (A) • Determine the Matrix M, the game matrix free of recessive rows and columns. M= • Find P*, the optimal strategy for the agency. P*= • Find Q*, the optimal strategy for the economy (fate). Q*= . Find v, the value of the game. v=$ (B) What proportion of each type of tour should be arranged for in advance in order for the agency to maximize its return irrespective of what the economy does the following year? (C) • • Standard: Luxury: What is the expected value of the game to the agency if they organize only luxury tours and fate plays strategy "down"? • The expected value is $ What is the expected value of the game if the agency plays its optimal strategy and fate plays the strategy "no change"? The expected value is $

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A tour agency organizes standard and luxury tours for the following year. Once the agency has committed to these tours, the schedule cannot be changed. The state of the economy during the following year has a direct effect on tour sales. From the past records the agency has established the following payoff matrix (in millions of dollars). Down Economy (Fate) No change Up Standard 1 Luxury 4 0 2 3 Complete parts (A) through (C) below. (A) • Determine the Matrix M, the game matrix free of recessive rows and columns. M= • Find P*, the optimal strategy for the agency. P*= • Find Q*, the optimal strategy for the economy (fate). Q*= . Find v, the value of the game. v=$ (B) What proportion of each type of tour should be arranged for in advance in order for the agency to maximize its return irrespective of what the economy does the following year? (C) • • Standard: Luxury: What is the expected value of the game to the agency if they organize only luxury tours and fate plays strategy "down"? • The expected value is $ What is the expected value of the game if the agency plays its optimal strategy and fate plays the strategy "no change"? The expected value is $
Transcribed Image Text:A tour agency organizes standard and luxury tours for the following year. Once the agency has committed to these tours, the schedule cannot be changed. The state of the economy during the following year has a direct effect on tour sales. From the past records the agency has established the following payoff matrix (in millions of dollars). Down Economy (Fate) No change Up Standard 1 Luxury 4 0 2 3 Complete parts (A) through (C) below. (A) • Determine the Matrix M, the game matrix free of recessive rows and columns. M= • Find P*, the optimal strategy for the agency. P*= • Find Q*, the optimal strategy for the economy (fate). Q*= . Find v, the value of the game. v=$ (B) What proportion of each type of tour should be arranged for in advance in order for the agency to maximize its return irrespective of what the economy does the following year? (C) • • Standard: Luxury: What is the expected value of the game to the agency if they organize only luxury tours and fate plays strategy "down"? • The expected value is $ What is the expected value of the game if the agency plays its optimal strategy and fate plays the strategy "no change"? The expected value is $
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