   Chapter 10, Problem 49RE ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Product design A playpen manufacturer wants to make a rectangular enclosure with maximum play area. To remain competitive, be wants the perimeter of the base to be only 16 feet. What dimensions should the playpen have?

To determine

To calculate: The dimensions the playpen should have if a playpen manufacturer wanted to make maximum play area of a rectangular enclosure, he wanted to make rectangular enclosure with the perimeter of the base to be only 16 feet for remain competitive.

Explanation

Given Information:

The provided information is he wants the perimeter of the base to be only 16 feet.

Formula Used:

The sides of a playpen are given as x and y, then the area of rectangular enclosure is:

A=xy

Calculation:

Consider the provided information is he wants the perimeter of the base to be only 16 feet.

In order to maximize the area, the following steps have to followed:

The area function is as follows:

When the sides of a playpen are given as x and y, then the area is:

A=xy

And,

The perimeter of the playpen is as follows:

2x+2y=16

Take out the value of y from the equation, which is,

Divide both sides by 2,

x+y=8

The value of y is:

y=8x

Put the value in the area equation:

A=x(8x)=8xx2

Take out the first derivative of the equation by the power rule,

A=ddx(8xx2)=ddx(8x)ddx(x2)=82x<

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