# Help: Optimization

• Feb 14th 2013, 11:07 AM
hailtopitt9
Help: Optimization
A box is to be made out of a 10 by 20 piece of cardboard. Squares of equal size will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top. Find the length L, width W, and height H of the resulting box that maximizes the volume. (Assume that Whttps://webwork.math.pitt.edu/webwor...144/char14.pngL ).

I am struggling with this homework problem, it would be appreciated if someone could help,
Thanks!
• Feb 14th 2013, 03:07 PM
chiro
Re: Help: Optimization
Hey hailtopitt9.

You are maximizing volume which is V = xyz.

Picture your box as a T-shape or a cross shape where you discard each of the four rectangles outside the cross shape.

By dividing the box into three parts for each side you get z+x+z=10 and z+y+z=20 or 2z+x = 10 and 2z+y=20 with V=xyz.

This gives you three equations in three variables which you can now solve.

If its still confusing, you might want to draw a diagram and look at how this is obtained.