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 h from the corners and folding up the sides as in the figure below:

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=1in. and that it is constructed using 124 in^2 of cardboard (i.e.,AB=124). Which values A and B maximize the volume? 

A=

B=

Answer 1

AB = 124

B = 124 / B

V = (A - 2)(B - 2)

V = (A - 2)((124 / A) - 2)

Expand and take first derivative equal to zero.