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 $
Chapter12: Sequences, Series And Binomial Theorem
Section12.3: Geometric Sequences And Series
Problem 12.58TI: What is the total effect on the economy of a government tax rebate of $500 to each household in...
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Transcribed Image Text:A tour agency organizes standard and luxury tours for the following year. Once the agency
has committed to these tours, the schedule cannot be changed. The state of the economy
during the following year has a direct effect on tour sales. From the past records the agency
has established the following payoff matrix (in millions of dollars).
Down
Economy (Fate)
No change
Up
Standard 1
Luxury
4
0
2
3
Complete parts (A) through (C) below.
(A)
• Determine the Matrix M, the game matrix free of recessive rows and columns.
M=
•
Find P*, the optimal strategy for the agency.
P*=
•
Find Q*, the optimal strategy for the economy (fate).
Q*=
. Find v, the value of the game.
v=$
(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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