Ostal regulations specify that a parcel sent by parcel post may have a combined length and girth (distance around) of no more than 126 inches. if a rectangular package has a square end, find the maximum volume of this package.

Let x represent the edge length of the square end. Then the area of the end of the package is x², and the length of the package is 126 -4x. The overall volume is ...
  V = x²×(126 -4x)
  V = -4x³ +126x²

The volume will be a maximum where the derivative of volume with respect to x is zero.
  V' = -12x² +252x
  V' = -12x(x -21)
This will be zero for x = 0 and for x = 21

The maximum volume of the package is
  V = (21 in)²(126 in -4×21 in)
  V = 18,522 in³