Question

A box is to be made out of a 8 by 16 piece of cardboard. Squares of equal size will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top. Find the length L, width W, and height H of the resulting box that maximizes the volume. (Assume that W≤L).

Answer 1

volume is \(V(x)=x(x-2x)(16-2x)\) multiply out, take the derivative, find the critical points etc