Question 487868
A manufacturer uses a 32 by 21 metal sheet to construct an open box by cutting out squares from each corner. What length square should be cut out to maximize the volume?
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Draw a picture of the 32 by 21 sheet.
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Draw the cut-outs that are x by x squares.
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The dimentions of the box are now:
length: 32-2x
width: 21-2x
height: x
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Volume = x(21-x)(32-x)
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To find the maximum volume, take the 
derivative of the cubic: dV/dx
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Set that equal to zero and solve to
find the value of "x" that gives you
the maximum volume.
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Cheers,
Stan H.