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Thu 4 Jan, 2007 07:51 pm
A cylindrical container costs $2.00 per square foot for the sides and $3.00 a square foot for the top and bottom. The container must hold 100 cubic feet of material. What are the dimensions of the most economical container.
I'm so glad I don't have to do math homework anymore.
cylindrical? or box shaped?
cost function (to be minimized) is
($3 * 2*pi*r^2) + ($2 * 2*pi*r*h)
V = pi*h*r^2 = 100
so h = 100/(pi*r^2)
that makes the cost function
($3 * 2*pi*r^2) + ($2 * 2*pi*r*100/(pi*r^2))
= $3 * 2*pi*r^2 + $2 * 2*100/r
= 6*pi*r^2 + 400/r (I dropped the $s here)
Find the value of r that minimizes the cost function. It's between 2.1 and 2.3.
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