   Chapter 10, Problem 50RE ### 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

# Printing design A page is to contain 56 square inches of print and have a 3 4 − inch margin at the bottom and 1-inch margins at the top and on both sides. Find the dimensions that minimize the size of the page (and hence the costs for paper).

To determine

To calculate: The dimensions that minimize the size of the page if a page is to contain 56 square inches of print, the page have a margin of 34-inch at the bottom and a margins of 1-inch at the top and on both sides.

Explanation

Given Information:

The provided information is a page is to contain 56 square inches of print and have a 34-inch margin at the bottom and 1-inch margins at the top and on both sides.

Formula Used:

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

A=xy

Calculation:

In order to minimize the area, the following steps have to follow:

As per the given information:

The area function is as follows:

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

A=(x+2)(y+74)

And,

As per the given information:

xy=56

Or,

y=56x

Put the value on the original area equation:

A=(x+2)(56x+74)

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

A=(x+2)ddx(56x+74)+(56x+74)ddx(x+2)=(x+2)(56x2)+(56x+74)

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