# A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base costs 31¢/square foot, the material for the sides costs 10¢/square foot, and the material for the top costs 19¢/square foot, determine the dimensions of the box that can be constructed at minimum cost.

Question

A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base costs 31¢/square foot, the material for the sides costs 10¢/square foot, and the material for the top costs 19¢/square foot, determine the dimensions of the box that can be constructed at minimum cost.

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Step 1

Given: help_outlineImage TranscriptioncloseVolume 20 ft Material cost for base = 31¢ per square foot Material cost for side = 10¢ per square foot. Material cost for top = 19¢ per square foot fullscreen
Step 2

Let the length, width and height of the rectangular box be x, x and y respectively. Then,

Step 3

The total cost is...

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### Calculus 