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A manufacturer is planning to sell a total of 500 machines to both foreign and domestic firms. The price the manufacturer can expect to receive for the machines will depend on the number of machines made available. It is estimated that if the manufacturer supplies x machines to the domestic market and y machines to the foreign market, the machines will 5y sell for 1200 - 3x + pesos per unit domestically, and 7 2200 - 2y + pesos per unit abroad. 2x 7 (a) Express the revenues from domestic and foreign markets as functions of x and y. Then show that the total revenue is given by R(x, y) = 1200x + 2200y - 3x² - 2y² + xy. (b) Evaluate Ry (100, 400) and interpret this value in the context of the problem. (c) Using Lagrange multipliers to maximize revenue, how many of the 500 machines should be sold domestically, and how many should be sold abroad? What is the maximum revenue?

A manufacturer is planning to sell a total of 500 machines to both foreign and domestic firms. The price the manufacturer can expect to receive for the machines will depend on the number of machines made available. It is estimated that if the manufacturer supplies x machines to the domestic market and y machines to the foreign market, the machines will 5y sell for 1200 - 3x + pesos per unit domestically, and 7 2200 - 2y + pesos per unit abroad. 2x 7 (a) Express the revenues from domestic and foreign markets as functions of x and y. Then show that the total revenue is given by R(x, y) = 1200x + 2200y - 3x² - 2y² + xy. (b) Evaluate Ry (100, 400) and interpret this value in the context of the problem. (c) Using Lagrange multipliers to maximize revenue, how many of the 500 machines should be sold domestically, and how many should be sold abroad? What is the maximum revenue?

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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A manufacturer is planning to sell a total of 500 machines to both foreign and domestic firms. The price the manufacturer can expect to receive for the machines will depend on the number of machines made available. It is estimated that if the manufacturer supplies x machines to the domestic market and y machines to the foreign market, the machines will 5y sell for 1200 - 3x + pesos per unit domestically, and 7 2x 2200 - 2y + pesos per unit abroad. 7 (a) Express the revenues from domestic and foreign markets as functions of x and y. Then show that the total revenue is given by R(x, y) = 1200x + 2200y - 3x² - 2y² + xy. (b) Evaluate R, (100, 400) and interpret this value in the context of the problem. (c) Using Lagrange multipliers to maximize revenue, how many of the 500 machines should be sold domestically, and how many should be sold abroad? What is the maximum revenue?
Transcribed Image Text:A manufacturer is planning to sell a total of 500 machines to both foreign and domestic firms. The price the manufacturer can expect to receive for the machines will depend on the number of machines made available. It is estimated that if the manufacturer supplies x machines to the domestic market and y machines to the foreign market, the machines will 5y sell for 1200 - 3x + pesos per unit domestically, and 7 2x 2200 - 2y + pesos per unit abroad. 7 (a) Express the revenues from domestic and foreign markets as functions of x and y. Then show that the total revenue is given by R(x, y) = 1200x + 2200y - 3x² - 2y² + xy. (b) Evaluate R, (100, 400) and interpret this value in the context of the problem. (c) Using Lagrange multipliers to maximize revenue, how many of the 500 machines should be sold domestically, and how many should be sold abroad? What is the maximum revenue?
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