Mathalina S.

asked • 10/15/16

An open box with its base having a length twice its width is to be constructed with 600 square cm of material. Find its dimensions that maximize the volume.

so I am asked to maximize l*w*h = 2w^2*h
l*w +2w*h+2lh=600
 
I solved for h in terms of w
2w*w+2wh+2*2wh=600
2wh+4wh=600-2w^2
h(6w)=600-2w^2
h=(600-2w^2)/(6w)
 
I plugged it into l*w*h and solved for w
2w*w*(600-2w^2)/(6w) = 0
(1200w^2-4w^4)/6w = 0
200w=2/3(w^2)
w=sqrt300
 
I know this is not the answer
where did I go wrong?

Michael J.

Where exactly is the box open from? The base or one of the sides? You did not specify.  Your answer depends on that open orientation.
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10/15/16

1 Expert Answer

By:

Mathalina S.

thank you
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10/16/16

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