Homework Help is Here – Start Your Trial Now!
Math
Calculus
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 3x machines will sell for 900- 6x + pesos per unit domestically, and 2400 - 5y + pesos per unit abroad. 2y 5 5 a) Express the revenues from domestic and foreign markets as functions of a and y. Then show that the total revenue is given by R(x, y)= 900x + 2400y - 6x² - 5y² + xy. ) Evaluate R, (100, 200) and interpret this value in the context of the problem. ) Using Lagrange multipliers to maximize revenue, how many of the 300 machines should be sold domestically, and how many should e 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 3x machines will sell for 900- 6x + pesos per unit domestically, and 2400 - 5y + pesos per unit abroad. 2y 5 5 a) Express the revenues from domestic and foreign markets as functions of a and y. Then show that the total revenue is given by R(x, y)= 900x + 2400y - 6x² - 5y² + xy. ) Evaluate R, (100, 200) and interpret this value in the context of the problem. ) Using Lagrange multipliers to maximize revenue, how many of the 300 machines should be sold domestically, and how many should e sold abroad? What is the maximum revenue?

Calculus: Early Transcendentals
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...
See similar textbooks
icon
Related questions
Question
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 z machines to the domestic market and y machines to the foreign market, the 2y machines will sell for 900- 6x + pesos per unit domestically, and 2400 - 5y + pesos per unit abroad. 3x 5 5 (a) Express the revenues from domestic and foreign markets as functions of a 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?
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 z machines to the domestic market and y machines to the foreign market, the 2y machines will sell for 900- 6x + pesos per unit domestically, and 2400 - 5y + pesos per unit abroad. 3x 5 5 (a) Express the revenues from domestic and foreign markets as functions of a 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?
Expert Solution
steps

Step by step

Solved in 7 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS