Chapter 10.4, Problem 21E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

** Minimum cost** The base of a rectangular box is to be twice as long as it is wide. The volume of the box is 256 cubic inches. The material for the top costs $0.10 per square inch and the material for the sides and bottom costs $0.05 per square inch. Find the dimensions that will make the cost a minimum.

To determine

**To calculate:** The dimensions to minimize the cost of the box.

Explanation

**Given Information:**

The volume of the box is

**Formula used:**

To find the minimum value, calculate the relevant stationary value of an equation. Differentiate the function with respect to the independent variable and equate it to

Check for local minima, then substituting the value of the independent variable will give the minimum value of the equation.

The power rule is used for a function in which the expression can be written as every term raised to a power (be it fractional, positive or negative). For the function

Volume of a rectangular box is given by:

**Calculation:**

Consider the provided statement,

The volume of the box is

Assume *l* is length, *b* is breadth or base and *h*is height

Thus, volume of the box is

When base is twice as long as the width, the volume

The cost for fencing is

In the equation

Use the equation for area

Apply the equation

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