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A storage box with a square base must have a volume of 80 cubic centimeters. The topand bottom cost $0.20 per square centimeter and the sides cost $0.10 per square centimeter.Find the dimensions that will minimize cost.

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.

check_circleAnswer
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 and height of the box be  y centimeters.

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

On substituting   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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Tagged in

Math

Calculus

Functions

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