# Yahoo Answers 4-19-14

- Author:
- Michael Brown

Suppose an airline policy states that all baggage must be box-shaped with a sum of...?
Suppose an airline policy states that all baggage must be box-shaped with a sum of length, width and height not exceeding 66 in. what are the dimensions and volume of a square based box with the greatest volume under these conditions?
I am asked to find
the length of the square-end edge in inches
the box height in inches
the volume of the box
Thank you in advance
Let x be the square edge length, h be the height
2x+h=66
h=66-2x
Volume=x^2(66-2x)=-2x^3+66x^2
Critical points are where the derivative equals zero
V'(x)=-6x^2+132x
-6x^2+132x=0
-6x(x-22)=0
x=0 or x=22
if x=22 inches, h=66-2x=66-2(22)=66-44=22 inches
the volume = 22*22*22=10648 cu in