   Chapter 4.7, Problem 13E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# A farmer wants to fence in an area of 1.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. How can he do this so as to minimize the cost of the fence?

To determine

To find: The process to minimize the cost of the fence.

Explanation

Given:

The area of the rectangular field = 1.5 million ft2 = 1,500,000 ft2 .

The farmer wants to put fence in the field by dividing it in half with a fence, parallel to one sides of the rectangle.

Calculation:

Let x be the length and y be the width (in feet) of the rectangular field.

In the Figure 1, the side EF of the rectangle is parallel to AB and BC, the sides of the rectangular field.

The area is xy=1500000 ft2.

y=1500000x .

The total length of the fence is made by 2 sides of length x and 3 sides of length y.

Then the total length of the fence is, T=2x+3y .

Substitute y=1500000x in T,

T=2x+31500000x

T=2x+4500000x

Differentiate T with respect to x ,

dTdx=24500000x2

For critical points, dTdx=0 .

24500000x2=02x2=4500000x2=2250000x=±2250000

Obtain the critical values as x=±1500

### 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

#### In Problems 33 – 38, solve each inequality. 36.

Mathematical Applications for the Management, Life, and Social Sciences 