SOLUTION: Today's question, please help 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 s

Question 460089: Today's question, please help
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. My answer was 5in is that correct?, if not, please help me with this. 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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