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