Yahoo Answers 4-19-14

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