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# Calculus/min/max optimization word problem

knoxy wrote at 2010-02-21 15:25:30
that solution is wrong. it should be to minimise the cost function and not the surface area of the pool. the cost function is 2*pi*(r^2) plus 2*pi*r*h which is then multiplied by price per square unit of the wood (which is a constant so does not effect the solution)

Skore wrote at 2014-12-17 02:32:28
Since the ceramic costs twice as much as the wood, that must be factored into the cost equation, which will look like this (x=radius):

2*pi*x^2+10/x

The rest of the steps in the solution are correct, so the answer will be X, or the radius, equals (5/2pi)^1/3

Calculus

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