SOLUTION: 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? Round answ

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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? Round answer to two decimal places.

I have tried this problems from many different angles, but I still cannot seem to get it right and I would love it if I could get some help. Thank you!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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.