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Math Help - Help: Optimization

  1. #1
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    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 WL ).

    I am struggling with this homework problem, it would be appreciated if someone could help,
    Thanks!
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  2. #2
    MHF Contributor
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    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.
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