- #1
tnutty
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Homework Statement
Johnny needs to make a rectangular box for his physics class project. He has bought P cm of wire and S cm^2 of special paper. He would like to use all the wire (for the 12 edges) and paper (for the 6 sides) to make the box.
What is the largest volume of the box that Johnny can make?
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One could use any method to solve the above problem.
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I just need help getting started.
First for the wire.
I think the perimeter function for the wire is : 4(x+2y) [ check my work please].
We are given S, the area of the paper. So a function for the paper might be, x^2
And we have the volume function for the box : V = xyz
So we have 3 functions :
Perimeter :z = 4(x+2y)
Area : y = x^2
Volume : V = xyz
From there I guess I can substitute. But I know something is wrong.
Any help solving this problem. Hints will be fine. Can I do this with double integrals?
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