document.write( "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?
\n" ); document.write( "This is the problem:
\n" ); document.write( "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?\r
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Algebra.Com's Answer #315636 by Alan3354(69443)\"\" \"About 
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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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\n" ); document.write( "Bending the long side means it will be 16 in long by some width.
\n" ); document.write( "W = 8 - 2x where x is the height, the amount bent up.
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\n" ); document.write( "If you meant 5 in on each side, that's greater than the 8 in of material.
\n" ); document.write( "W = 8 - 2x
\n" ); document.write( "V = 16*(8-2x)*x
\n" ); document.write( "V = 128x - 32x^2
\n" ); document.write( "The max is the vertex of the parabola f(x) = -32x^2 + 128x
\n" ); document.write( "The vertex is on the line of symmetry x = -b/2z = -128/-64
\n" ); document.write( "LOS is x = 2
\n" ); document.write( "Max volume is made by folding up 2 in on each side.
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\n" ); document.write( "Max = f(2) = 128*2 - 32*4
\n" ); document.write( "Max = 128 cubic inches
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