Gabriel A.

asked • 05/02/17

Find the dimensions of the open rectangular box of maximum volume

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 43 in. by 23 in. by cutting congruent squares from the corners and folding up the sides. Then find the volume.

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Mark M. answered • 05/02/17

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V = (43 - 2h)(23 - 2h)h
 
Can you multiply and differentiate?
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Gabriel A.

no, i forgot how to do any of this
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05/02/17

Mark M.

V= 989h - 112h2 + 4h3
V' = 989 - 224h + 12h2
 
Maximum occurs at
 
0 = 12h2 - 224h + 989
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05/02/17

Gabriel A.

it's asking for the dimensions of the L, W and H, but i already got the answer, your calculations were wrong btw
 
 
V(h) = 4h³ - 132h² + 989h
V '(h) = 12h² - 264h + 989 
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05/02/17

Mark M.

You are welcome!
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05/02/17

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