Application - Optimization

Question

A box (with no top) is to be constructed from a piece of cardboard of sides A and B by cutting out squares of length h from the corners and folding up the sides as in the figure below:

Suppose that the box height is h=5 in. and that it is constructed using 138 in.2 of cardboard (i.e., AB=138). Which values A and B maximize the volume?

A=  in.

B=  in.

Answer 1

V(A) = 5(A - 10)((138 / A) - 10)

Simpify, determine V'(a), set equal to 0, calculate A, then B