The base and top of a can costs 10 cents per square inch, and the side costs 15

Question

The base and top of a can costs 10 cents per square inch, and the side costs 15 cents per square inch. The cost to build the can is the cost of the bottom and top plus the cost of the side, so the cost is given by the expression 10*(2pix^2)+15(2pixh) where x is the radius of the base of the can and h is the height. The volume of the can is V=pix^2h.

a.) If the volume of the can is a fixed constant V, show that the total cost to build the can for x>0 is given by the function C(x)=20pix^2+(30V/x).

Explanation / Answer

V = x2h -> h = V/(x2)

Therefore:

C(x) = 10(2x2) + 15(2xh) = 20x2 + 30xh =

20x2 + 30x(V/(x2)) =

20x2 + 30V/x

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