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rica is p = 29 - 0.2x (for 0 sxs 145), the price function for cars sold in Europe is q = 13 - 0.1y (for 0sys 130), and the price function fo is r= 15 - 0.1z (for 0 szs 150), all in thousands of dollars, where x, y, and z are the numbers of cars sold in America, Europe, and Asia, re company's cost function is C = 20 + 7(x + y + z) thousand dollars. Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asi costs, where each revenue is price times quantity.] P(x, y, z) = Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials P, P and P, equal to zero and solve. As the maximum exists, it must occur at this point.] America

rica is p = 29 - 0.2x (for 0 sxs 145), the price function for cars sold in Europe is q = 13 - 0.1y (for 0sys 130), and the price function fo is r= 15 - 0.1z (for 0 szs 150), all in thousands of dollars, where x, y, and z are the numbers of cars sold in America, Europe, and Asia, re company's cost function is C = 20 + 7(x + y + z) thousand dollars. Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asi costs, where each revenue is price times quantity.] P(x, y, z) = Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials P, P and P, equal to zero and solve. As the maximum exists, it must occur at this point.] America

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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An automobile manufacturer sells cars in America, Europe, and Asia, charging a different price in each of the three markets. The price function for cars sold in America is p = 29 - 0.2x (for 0 s xs 145), the price function for cars sold in Europe is q = 13 - 0.1y (for 0 sys 130), and the price function for cars sold in Asia is r= 15 - 0.1z (for 0 szs 150), all in thousands of dollars, where x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively. The company's cost function is C = 20 + 7(x + y + z) thousand dollars. (a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.] P(x, y, z) = (b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials P, P and P, equal to zero and solve. Assuming that the maximum exists, it must occur at this point.] America Europe Asia
Transcribed Image Text:An automobile manufacturer sells cars in America, Europe, and Asia, charging a different price in each of the three markets. The price function for cars sold in America is p = 29 - 0.2x (for 0 s xs 145), the price function for cars sold in Europe is q = 13 - 0.1y (for 0 sys 130), and the price function for cars sold in Asia is r= 15 - 0.1z (for 0 szs 150), all in thousands of dollars, where x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively. The company's cost function is C = 20 + 7(x + y + z) thousand dollars. (a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.] P(x, y, z) = (b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials P, P and P, equal to zero and solve. Assuming that the maximum exists, it must occur at this point.] America Europe Asia
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