Chapter 10, Problem 49RE

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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:

**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:

And,

The perimeter of the playpen is as follows:

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

Divide both sides by 2,

The value of *y* is:

Put the value in the area equation:

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

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