Question

A storage box with a square base must have a volume of 80 cubic centimeters. The top

and bottom cost $0.20 per square centimeter and the sides cost $0.10 per square centimeter.

Find the dimensions that will minimize cost.

Step 1

To find the dimension of the storage box that will minimize the cost.

Step 2

Given the storage box has volume 80 cubic centimeter with square base.

The cost of the top to bottom of the box is $0.20 per square centimeter and cost of side of the box is $0.10 per square centimeter.

Consider the length and width be *x *and height of the box be *y* centimeters.

The volume of the box is given by *V=length*width*height*.

On substituting *x * for length and width and *y* for height the volume of the box will be *V=x^2y*.

The box has volume 80 cubic centimeter then 80*=x^2y * …… (1)

Calculate the area and cost of the construction of top, bottom and sides of the box as follows.

Step 3

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