Soju H.

asked • 11/13/18

An Optimization Problem

I have some issues regarding this optimization problem


A cylindrical garbage can with no top needs to hold 6 ft3 of garbage. What diomensions should the can have in order to minimize the amount of material needed to manufacture it?


Volume = (pi)(r2)(height) ; Surface Area(SA) = 2(pi)(r)(h) + (pi)(r2)


I set height = 6/(pi)(r2) from the volume equation and the given volume (6 ft3)


Do I just plug this h value into the Surface Area equation and then take a derivative of it?

John M.

You have 2 variables, r and h. You might just graph the equation for r and h as x and y, and generate a chart. Set r= 1, find h, set r=2, etc.
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12/16/19

1 Expert Answer

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Larry S. answered • 05/26/20

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