A manufacturer is planning to sell a total of 300 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 a machines to the domestic market and y machines to the foreign market, the machines will sell for 2y 3x 900 - 6x + pesos per unit domestically, and 2400 - 5y + pesos per 5 unit abroad. 5 (a) Express the revenues from domestic and foreign markets as functions of and y. Then show that the total revenue is given by R(x, y) = 900x+2400y - 6x² - 5y² + xy. (b) Evaluate R (100, 200) and interpret this value in the context of the problem. (c) Using Lagrange multipliers to maximize revenue, how many of the 300 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 300 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 a machines to the domestic market and y machines to the foreign market, the machines will sell for 2y 3x 900 - 6x + pesos per unit domestically, and 2400 - 5y + pesos per 5 unit abroad. 5 (a) Express the revenues from domestic and foreign markets as functions of and y. Then show that the total revenue is given by R(x, y) = 900x+2400y - 6x² - 5y² + xy. (b) Evaluate R (100, 200) and interpret this value in the context of the problem. (c) Using Lagrange multipliers to maximize revenue, how many of the 300 machines should be sold domestically, and how many should be sold abroad? What is the maximum revenue?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A manufacturer is planning to sell a total of 300 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 sell for
3x
2y
900 - 6x + pesos per unit domestically, and 2400 - 5y + pesos per
5
5
unit abroad.
(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) = 900x + 2400y - 6x² - 5y² + xy.
(b) Evaluate R (100, 200) and interpret this value in the context of the problem.
(c) Using Lagrange multipliers to maximize revenue, how many of the 300 machines
should be sold domestically, and how many should be sold abroad? What is the
maximum revenue?
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