A firm is producing cylindrical containers to contain a given volume. Suppose that the top and bottom are made of a material that is $N$ times as expensive as the material used for the side of the cylinder, which has a cost of $C$ per unit area. Find, in terms of $N$, the ratio of height to base radius of the cylinder that minimises the cost of producing the containers.
I am not too sure how to go about answering this. I was thinking that you might use the volume of a cylinder formula as a function and then get the partial derivative with respect to the radius, and the height. But I would have no idea what to do with these derivatives or even if that is the right thing to do. I am assuming that it is, as it is from a module in multivariable calculus.