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.
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
The cost is
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.