Explanation Given information: f ( x , y ) = 3 x − 2 y g ( x . y ) = x 2 + 2 y 2 − 44 Formula used: The Lagrange function is L ( x , y ) = f ( x , y ) − λ g ( x , y ) . Calculation: The Lagrange function is L ( x , y ) = f ( x , y ) − λ g ( x , y ) L ( x , y ) = 3 x − 2 y − λ ( x 2 + 2 y 2 − 44 ) L ( x , y ) = 3 x − 2 y − λ x 2 − 2 λ y 2 + 44 λ The 1 st order partial derivatives are as below, L x = 3 − 2 x λ L y = − 2 − 4 y λ The system equations are, L x = 0 ; L y = 0 ; g ( x , y ) = 0 3 − 2 x λ = 0 ⇒ 3 = 2 x λ ⇒ λ = 3 2 x − 2 − 4 y λ = 0 ⇒ − 2 = 4 y λ ⇒ λ = − 1 2 y Since the left hand side is λ , so right hand sides of these equations are equal to each other

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

See similar textbooks

Videos

Question

Chapter 8.6, Problem 6P

To determine

To find:

The maximum or minimum values of f(x,y) using Lagrange multipliers.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.6, Problem 5P

Chapter 8.6, Problem 7P

Students have asked these similar questions

The function f(x,y) = 4x + 4y has an absolute maximum value and absolute minimum value subject to the constraint 9x - 9xy + 9y = 1. Use Lagrange multipliers to find these values. The absolute maximum value is (Type an exact answer.)

A gadget manufacturer has developed a profit model that depends on x number of gadgets per month sold and y hours per month of advertising, according to the function P(x, y) = 9x2 + 36xy − 4y2 − 18x − 18y, where P is measured in thousand dollars. If the budgetary constraint is 3x + 4y = 32, use the method of Lagrange Multipliers to find the maximum profit.

Please give a clear and detailed solution. Use Lagrange multipliers to find the maximum and minimum values of this function subject to the constraint.

Chapter 8 Solutions

APPLIED CALCULUS (WILEY PLUS)

Ch. 8.1 - Prob. 1P Ch. 8.1 - Prob. 2P Ch. 8.1 - Prob. 3P Ch. 8.1 - Prob. 4P Ch. 8.1 - Prob. 5P Ch. 8.1 - Prob. 6P Ch. 8.1 - Prob. 7P Ch. 8.1 - Prob. 8P Ch. 8.1 - Prob. 9P Ch. 8.1 - Prob. 10P

Ch. 8.1 - Prob. 11P Ch. 8.1 - Prob. 12P Ch. 8.1 - Prob. 13P Ch. 8.1 - Prob. 14P Ch. 8.1 - Prob. 15P Ch. 8.1 - Prob. 16P Ch. 8.1 - Prob. 17P Ch. 8.1 - Prob. 18P Ch. 8.1 - Prob. 19P Ch. 8.1 - Prob. 20P Ch. 8.1 - Prob. 21P Ch. 8.1 - Prob. 22P Ch. 8.1 - Prob. 23P Ch. 8.1 - Prob. 24P Ch. 8.1 - Prob. 25P Ch. 8.1 - Prob. 26P Ch. 8.1 - Prob. 27P Ch. 8.1 - Prob. 28P Ch. 8.1 - Prob. 29P Ch. 8.1 - Prob. 30P Ch. 8.2 - Prob. 1P Ch. 8.2 - Prob. 2P Ch. 8.2 - Prob. 3P Ch. 8.2 - Prob. 4P Ch. 8.2 - Prob. 5P Ch. 8.2 - Prob. 6P Ch. 8.2 - Prob. 7P Ch. 8.2 - Prob. 8P Ch. 8.2 - Prob. 9P Ch. 8.2 - Prob. 10P Ch. 8.2 - Prob. 11P Ch. 8.2 - Prob. 12P Ch. 8.2 - Prob. 13P Ch. 8.2 - Prob. 14P Ch. 8.2 - Prob. 15P Ch. 8.2 - Prob. 16P Ch. 8.2 - Prob. 17P Ch. 8.2 - Prob. 18P Ch. 8.2 - Prob. 19P Ch. 8.2 - Prob. 20P Ch. 8.2 - Prob. 21P Ch. 8.2 - Prob. 22P Ch. 8.2 - Prob. 23P Ch. 8.2 - Prob. 24P Ch. 8.2 - Prob. 25P Ch. 8.2 - Prob. 26P Ch. 8.2 - Prob. 27P Ch. 8.2 - Prob. 28P Ch. 8.2 - Prob. 29P Ch. 8.2 - Prob. 30P Ch. 8.2 - Prob. 31P Ch. 8.2 - Prob. 32P Ch. 8.2 - Prob. 33P Ch. 8.2 - Prob. 34P Ch. 8.2 - Prob. 35P Ch. 8.2 - Prob. 36P Ch. 8.2 - Prob. 37P Ch. 8.2 - Prob. 38P Ch. 8.2 - Prob. 39P Ch. 8.2 - Prob. 40P Ch. 8.2 - Prob. 41P Ch. 8.2 - Prob. 42P Ch. 8.2 - Prob. 43P Ch. 8.2 - Prob. 44P Ch. 8.3 - Prob. 1P Ch. 8.3 - Prob. 2P Ch. 8.3 - Prob. 3P Ch. 8.3 - Prob. 4P Ch. 8.3 - Prob. 5P Ch. 8.3 - Prob. 6P Ch. 8.3 - Prob. 7P Ch. 8.3 - Prob. 8P Ch. 8.3 - Prob. 9P Ch. 8.3 - Prob. 10P Ch. 8.3 - Prob. 11P Ch. 8.3 - Prob. 12P Ch. 8.3 - Prob. 13P Ch. 8.3 - Prob. 14P Ch. 8.3 - Prob. 15P Ch. 8.3 - Prob. 16P Ch. 8.3 - Prob. 17P Ch. 8.3 - Prob. 18P Ch. 8.3 - Prob. 19P Ch. 8.3 - Prob. 20P Ch. 8.3 - Prob. 21P Ch. 8.3 - Prob. 22P Ch. 8.3 - Prob. 23P Ch. 8.3 - Prob. 24P Ch. 8.3 - Prob. 25P Ch. 8.3 - Prob. 26P Ch. 8.3 - Prob. 27P Ch. 8.3 - Prob. 28P Ch. 8.3 - Prob. 29P Ch. 8.3 - Prob. 30P Ch. 8.3 - Prob. 31P Ch. 8.3 - Prob. 32P Ch. 8.3 - Prob. 33P Ch. 8.3 - Prob. 34P Ch. 8.3 - Prob. 35P Ch. 8.3 - Prob. 36P Ch. 8.3 - Prob. 37P Ch. 8.3 - Prob. 38P Ch. 8.3 - Prob. 39P Ch. 8.3 - Prob. 40P Ch. 8.4 - Prob. 1P Ch. 8.4 - Prob. 2P Ch. 8.4 - Prob. 3P Ch. 8.4 - Prob. 4P Ch. 8.4 - Prob. 5P Ch. 8.4 - Prob. 6P Ch. 8.4 - Prob. 7P Ch. 8.4 - Prob. 8P Ch. 8.4 - Prob. 9P Ch. 8.4 - Prob. 10P Ch. 8.4 - Prob. 11P Ch. 8.4 - Prob. 12P Ch. 8.4 - Prob. 13P Ch. 8.4 - Prob. 14P Ch. 8.4 - Prob. 15P Ch. 8.4 - Prob. 16P Ch. 8.4 - Prob. 17P Ch. 8.4 - Prob. 18P Ch. 8.4 - Prob. 19P Ch. 8.4 - Prob. 20P Ch. 8.4 - Prob. 21P Ch. 8.4 - Prob. 22P Ch. 8.4 - Prob. 23P Ch. 8.4 - Prob. 24P Ch. 8.4 - Prob. 25P Ch. 8.4 - Prob. 26P Ch. 8.4 - Prob. 27P Ch. 8.4 - Prob. 28P Ch. 8.4 - Prob. 29P Ch. 8.4 - Prob. 30P Ch. 8.4 - Prob. 31P Ch. 8.4 - Prob. 32P Ch. 8.4 - Prob. 33P Ch. 8.4 - Prob. 34P Ch. 8.4 - Prob. 35P Ch. 8.4 - Prob. 36P Ch. 8.4 - Prob. 37P Ch. 8.4 - Prob. 38P Ch. 8.4 - Prob. 39P Ch. 8.4 - Prob. 40P Ch. 8.4 - Prob. 41P Ch. 8.4 - Prob. 42P Ch. 8.4 - Prob. 43P Ch. 8.4 - Prob. 44P Ch. 8.5 - Prob. 1P Ch. 8.5 - Prob. 2P Ch. 8.5 - Prob. 3P Ch. 8.5 - Prob. 4P Ch. 8.5 - Prob. 5P Ch. 8.5 - Prob. 6P Ch. 8.5 - Prob. 7P Ch. 8.5 - Prob. 8P Ch. 8.5 - Prob. 9P Ch. 8.5 - Prob. 10P Ch. 8.5 - Prob. 11P Ch. 8.5 - Prob. 12P Ch. 8.5 - Prob. 13P Ch. 8.5 - Prob. 14P Ch. 8.5 - Prob. 15P Ch. 8.5 - Prob. 16P Ch. 8.5 - Prob. 17P Ch. 8.5 - Prob. 18P Ch. 8.5 - Prob. 19P Ch. 8.5 - Prob. 20P Ch. 8.5 - Prob. 21P Ch. 8.5 - Prob. 22P Ch. 8.5 - Prob. 23P Ch. 8.5 - Prob. 24P Ch. 8.5 - Prob. 25P Ch. 8.5 - Prob. 26P Ch. 8.5 - Prob. 27P Ch. 8.5 - Prob. 28P Ch. 8.5 - Prob. 29P Ch. 8.5 - Prob. 30P Ch. 8.5 - Prob. 31P Ch. 8.5 - Prob. 32P Ch. 8.6 - Prob. 1P Ch. 8.6 - Prob. 2P Ch. 8.6 - Prob. 3P Ch. 8.6 - Prob. 4P Ch. 8.6 - Prob. 5P Ch. 8.6 - Prob. 6P Ch. 8.6 - Prob. 7P Ch. 8.6 - Prob. 8P Ch. 8.6 - Prob. 9P Ch. 8.6 - Prob. 10P Ch. 8.6 - Prob. 11P Ch. 8.6 - Prob. 12P Ch. 8.6 - Prob. 13P Ch. 8.6 - Prob. 14P Ch. 8.6 - Prob. 15P Ch. 8.6 - Prob. 16P Ch. 8.6 - Prob. 17P Ch. 8.6 - Prob. 18P Ch. 8.6 - Prob. 19P Ch. 8.6 - Prob. 20P Ch. 8.6 - Prob. 21P Ch. 8.6 - Prob. 22P Ch. 8.6 - Prob. 23P Ch. 8.6 - Prob. 24P Ch. 8.6 - Prob. 25P Ch. 8.6 - Prob. 26P Ch. 8.6 - Prob. 27P Ch. 8 - Prob. 1SYU Ch. 8 - Prob. 2SYU Ch. 8 - Prob. 3SYU Ch. 8 - Prob. 4SYU Ch. 8 - Prob. 5SYU Ch. 8 - Prob. 6SYU Ch. 8 - Prob. 7SYU Ch. 8 - Prob. 8SYU Ch. 8 - Prob. 9SYU Ch. 8 - Prob. 10SYU Ch. 8 - Prob. 11SYU Ch. 8 - Prob. 12SYU Ch. 8 - Prob. 13SYU Ch. 8 - Prob. 14SYU Ch. 8 - Prob. 15SYU Ch. 8 - Prob. 16SYU Ch. 8 - Prob. 17SYU Ch. 8 - Prob. 18SYU Ch. 8 - Prob. 19SYU Ch. 8 - Prob. 20SYU Ch. 8 - Prob. 21SYU Ch. 8 - Prob. 22SYU Ch. 8 - Prob. 23SYU Ch. 8 - Prob. 24SYU Ch. 8 - Prob. 25SYU Ch. 8 - Prob. 26SYU Ch. 8 - Prob. 27SYU Ch. 8 - Prob. 28SYU Ch. 8 - Prob. 29SYU Ch. 8 - Prob. 30SYU Ch. 8 - Prob. 31SYU Ch. 8 - Prob. 32SYU Ch. 8 - Prob. 33SYU Ch. 8 - Prob. 34SYU Ch. 8 - Prob. 35SYU Ch. 8 - Prob. 36SYU Ch. 8 - Prob. 37SYU Ch. 8 - Prob. 38SYU Ch. 8 - Prob. 39SYU Ch. 8 - Prob. 40SYU Ch. 8 - Prob. 41SYU Ch. 8 - Prob. 42SYU Ch. 8 - Prob. 43SYU Ch. 8 - Prob. 44SYU Ch. 8 - Prob. 45SYU Ch. 8 - Prob. 46SYU Ch. 8 - Prob. 47SYU Ch. 8 - Prob. 48SYU Ch. 8 - Prob. 49SYU Ch. 8 - Prob. 50SYU Ch. 8 - Prob. 51SYU Ch. 8 - Prob. 52SYU Ch. 8 - Prob. 53SYU Ch. 8 - Prob. 54SYU Ch. 8 - Prob. 55SYU Ch. 8 - Prob. 56SYU Ch. 8 - Prob. 57SYU Ch. 8 - Prob. 58SYU Ch. 8 - Prob. 59SYU Ch. 8 - Prob. 60SYU Ch. 8 - Prob. 1FOT Ch. 8 - Prob. 2FOT Ch. 8 - Prob. 3FOT Ch. 8 - Prob. 4FOT Ch. 8 - Prob. 5FOT Ch. 8 - Prob. 6FOT Ch. 8 - Prob. 7FOT

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Algebra for College Students
Algebra
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning

Algebra: Structure And Method, Book 1

Algebra

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:McDougal Littell

Algebra for College Students

Algebra

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:9781285463247

Author:David Poole

Publisher:Cengage Learning

SEE MORE TEXTBOOKS

Solve ANY Optimization Problem in 5 Steps w/ Examples. What are they and How do you solve them?; Author: Ace Tutors;https://www.youtube.com/watch?v=BfOSKc_sncg;License: Standard YouTube License, CC-BY

Optimization Problems in Calculus; Author: Professor Dave Explains;https://www.youtube.com/watch?v=q1U6AmIa_uQ;License: Standard YouTube License, CC-BY

Introduction to Optimization; Author: Math with Dr. Claire;https://www.youtube.com/watch?v=YLzgYm2tN8E;License: Standard YouTube License, CC-BY

The maximum or minimum values of f ( x , y ) using Lagrange multipliers.

Solution Summary: The author explains how to find the maximum and minimum values of f(x,y) using Lagrange multipliers.

Videos

To find:

The maximum or minimum values of f(x,y) using Lagrange multipliers.

Want to see the full answer?

Chapter 8 Solutions

The maximum or minimum values of f ( x , y ) using Lagrange multipliers.

Solution Summary: The author explains how to find the maximum and minimum values of f(x,y) using Lagrange multipliers.

Videos

To find: The maximum or minimum values of f(x,y) using Lagrange multipliers.

Want to see the full answer?

Chapter 8 Solutions

To find:

The maximum or minimum values of f(x,y) using Lagrange multipliers.