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Minimizing Surface Area

A container company is going to construct a shipping container of volume 12 ft3 with a square bottom and a square top. The cost of the top and sides is $2 per square foot and for the bottom is $3 per square foot. What dimensions will minimize the cost of the container.

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Assume that the length of each side of the square bottom is x. Assume that the height is y. Then we know that the volume is
x^2*y=12 ........................(1)
The cost is


Solution Summary

Surface area of a container is minimized using derivatives. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.