Chapter 7.6, Problem 40E

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

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

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

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Office Space Partitions will be used in an office to form four equal work areas with a total area of 360 square feet (see figure). The partitions that are x feet long cost $100 per foot and the partitions that are y feet long cost$120 per foot.(a) Find the dimensions x and y that will minimize the cost of the partitions.(b) What is the minimum cost?

(a)

To determine

To calculate: The dimension x and y that will minimize the cost of the partitions.

Explanation

Given Information:

Partitions will be used in an office to form four equal work areas with a total area of 360 square feet. the partitions that are x feet long cost $100 per foot and the partitions that are y feet long cost$120 per foot and the provided figure is:

Formula used:

Method of Lagrange multipliers,

If the function f(x,y) contains a maximum or minimum subject to the constraint g(x,y)=0

Then the maximum or minimum can occur at one of the critical numbers of the function F is,

F(x,y,λ)=f(x,y)λg(x,y) where, λ is a Lagrange multiplier.

Steps to determine the minimum or maximum of the function f.

1. Solve the system of equations,

Fx(x,y,λ)=0Fy(x,y,λ)=0Fλ(x,y,λ)=0

2. Determine the value of the function f at each solution obtained from the step 1.

The largest value gives the maximum value of function f subject to the constraint g(x,y)=0 and the lowest value gives the minimum value of function f subject to the constraint g(x,y)=0.

Calculation:

As given, total area of 360 square feet. the partitions that are x feet long cost $100 per foot and the partitions that are y feet long cost$120 per foot

(b)

To determine

To calculate: The minimum cost of fencing.

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