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I'm working on optimization problems right now, and let me tell ya, if you thought I was horrible at everything else wait until you see me attempt one of these :grumpy: I have three questions but I'm hoping if I just get help with the one I will be able to get the processes for the rest on my own. Here it goes:

A rectangular storage container with an open top is to have a volume of 10m^3. The length of the base is twice that of the width. Material for the base costs $10 per square meter and and $6 per square meter for the side. Find the cost of materials for the cheapest such container :yuck:

OK So first off all I wrote down all my givens and drew myself a little picture which I had hoped would help me visualize the problem. Now I know that the volume of the container is 10 and that V=LWH, but that the length is twice the width allowing me to get rid of one of the variables. Leaving me with 10=2w^2 *h. Ic ould then get rid of the h by saying that h=(5/w^2).

P=2l +2w +h

P = 2(2w) +2w +5/w^2

At this point I end up getting weird numbers, I have a feeling that part of the problem is that I never factored in that the box has an open top but I'm not sure how to go about doing that. I've tried to show what I've done and my reasons for doing it, but unfortunately I know its wrong. Any help you can give I would really appreciate, thanks a lot!

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# Calculus Optimization problems

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