A parcel delivery service will deliver packages only if the length plus the girth (distance around, taken perpendicular to the length) does not exceed 112 inches. Find the maximum volume of a rectangular box with square ends that satisfies the delivery company's requirements.

Answer 1

clearly the maximum volume will happen with a value of 112. So,
x^2+y = 112
v = x^2y = x^2(112-x^2)
now just find where dv/dx = 0

Answer 2

oops. I did the girth wrong. It is 4x, not x^2. 4x+y = 112
v = x^2(112-4x)