Calculus Meltdown --- Need Help!

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Discus: SAT/ACT Tests and Test Preparation: May 2004 Archive: Calculus Meltdown --- Need Help!
By Netshark2005 (Netshark2005) on Monday, May 17, 2004 - 12:55 pm: Edit

Hi, I'm stuck on this one calculus word problem, from the chapter about Application of Derivatives. Here's the question:
Find the dimensions of the largest open-top storage bin with a square base and vertical sides that can be made from 108 square feet of sheet steel. (Neglect the thickness of the steel and assume that there is no waste)
Thanks for the help!

By Optimizerdad (Optimizerdad) on Monday, May 17, 2004 - 01:42 pm: Edit

How about starting with a hint?

Let x= side of square base and y=height. Then,
V = volume of bin = x *x * y
and A = total area
= x*x (base) + 4xy (4 sides)
= 108.
Get y as a function of x from this last equation, plug into the formula for volume, then find x that maximizes V.

Have a field day... :-)

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