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?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54949e7f-dcb8-4293-b304-1543d1cac238%2F8a2c1b56-9602-42ac-ba86-5a4130b52e37%2Ftzrzdpi_processed.jpeg&w=3840&q=75)
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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