Applications of Maxima and Minima Problems

Question

. The volume of an open box with a square base is 8, 000 cubic centimeter. Find the dimensions of the box if the material used to make the box is a minimum.

Answer 1

Let x = length of a side of the base and let y = height

Then x²y = 8000. So y = 8000 / x²

Minimize S = x² + 4xy = x² + 32000 / x

Now, set S' = 0 and solve for x.