   Chapter 7.6, Problem 22E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

# Finding Positive Numbers In Exercises 19-22, find three positive numbers x, y, and z that satisfy the given conditions.The sum is 36 and the sum of the cubes is a minimum.

To determine

To calculate: The three positive numbers x,yandz that satisfy this statement “The sum is 36 and sum of the cube is minimum”.

Explanation

Given Information:

The sum is 36 and sum of the cube is minimum.

Formula used:

Lagrange Multiplier:

F(x,y,z)=f(x,y,z)λg(x,y,z)

Where f(x,y,z)andλg(x,y,z) are the function and the constraint and λ is the Lagrange Multiplier.

Step 1: Consider the number to be x,yandz.

Step 2: Write the function and constraint in the expansion.

Step 3: Partially differentiate f and g with respect to x,yandz.

Step 4: Use the primary formula, find the value of λ.

Step 5: Using λ find the relation between the numbers and arrive at the final form.

Step 6: Substitute the values in the g to find all the three numbers.

Calculation:

Consider the three positive numbers be x,y,z.

Minimize f(x,y,z)=x3+y3+z3 subject to g(x,y,z)=x+y+z=36.

The gradients of f and g are found by solving the system of equations.

F(x,y,z)=f(x,y,z)λg(x,y,z)=x3+y3+z3λ(x+y+z36)=x3+y3+z3

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Sketch the graph of the set. 39. {(x, y) | y x2 1}

Single Variable Calculus: Early Transcendentals, Volume I

#### Evaluate: a. 2332 b. [(13)3]1/3

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In problems 37-44, perform the indicated operations and simplify. 39.

Mathematical Applications for the Management, Life, and Social Sciences

#### True or False: converges conditionally.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 