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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 Sxs 145), the price function for cars sold in Europe is q = 18 - 0.1y (for 0sys 180), and the price function for cars sold in Asia is r= 19 - 0.1z (for 0 s z s 190), 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 = 23 + 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

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 Sxs 145), the price function for cars sold in Europe is q = 18 - 0.1y (for 0sys 180), and the price function for cars sold in Asia is r= 19 - 0.1z (for 0 s z s 190), 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 = 23 + 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

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 37CR
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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 sxs 145), the price function for cars sold in Europe is g = 18 - 0.1y (for 0 sys 180), and the price function for cars sold in Asia isr = 19 - 0.1z (for 0 szs 190), 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 = 23 + 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 sxs 145), the price function for cars sold in Europe is g = 18 - 0.1y (for 0 sys 180), and the price function for cars sold in Asia isr = 19 - 0.1z (for 0 szs 190), 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 = 23 + 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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