A tour agency organizes special 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 past records the company has established the following payoff matrix (in millions of dollars): (A) Find optimal strategies for both the company and fate (the economy). What is the value of the game? (B) What proportion of each type of tour should be arranged for i? advance in order for the company to maximize its return irrespective of what the economy does the following year? (C) What is the expected value of the game to the company if they organize only luxury tours and fate plays the strategy "Down"? If the company plays its optimal strategy and fate plays the strategy "No change"?

Economy (Fate) 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 Down No change Up year has a direct effect on tour sales. From past records the agency has established the following payoff matrix (in millions of dollars). Complete parts (A) through (C) below. Standard 5 O Luxury N (A) Find optimal strategies for both the agency and fate (the economy). What is the value of the game? Determine the matrix M, the game matrix free of recessive rows and columns. M =] (Type an integer or simplified fraction for each matrix element.) Find P , the optimal strategy for the agency. P* =0 (Type an integer or simplified fraction for each matrix element.) Find Q , the optimal strategy for the economy (fate). Q = ] (Type an integer or simplified fraction for each matrix element.) 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? Standard: (Type an integer or a simplified fraction.) Luxury: (Type an integer or a simplified fraction.) (C) What is the expected value of the game to the agency if they organize only luxury tours and fate plays the strategy "down"? The expected value is $ (Round to the nearest dollar as needed.) What is the expected value of the game to the agency if the agency plays its optimal strategy and fate plays the strategy "no change"? The expected value is $ (Round to the nearest dollar as needed.)