SOLUTION: I have this word problem that driving me nuts, the answer I got was forty inches and I know that can't be right? Can someone help me? This is the problem: Economite Plastics plan

Question 460186: I have this word problem that driving me nuts, the answer I got was forty inches and I know that can't be right? Can someone help me?
This is the problem:
Economite Plastics plans to produce a one-compartment vertical filey by handling the long side of an 8-in by 16 in. sheet of plast along two lines to form a U shape. How tall should the file be in order to maximize the volume that the file can hold?
Thanks
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A one compartment vertical file is t be constructed by bending the long side of an 8in by 16 in plastic along two lines to form a U shape. How tall should the file be to maximize the volume that it can hold.
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Bending the long side means it will be 16 in long by some width.
W = 8 - 2x where x is the height, the amount bent up.
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If you meant 5 in on each side, that's greater than the 8 in of material.
W = 8 - 2x
V = 16*(8-2x)*x
V = 128x - 32x^2
The max is the vertex of the parabola f(x) = -32x^2 + 128x
The vertex is on the line of symmetry x = -b/2z = -128/-64
LOS is x = 2
Max volume is made by folding up 2 in on each side.
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Max = f(2) = 128*2 - 32*4
Max = 128 cubic inches

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