A copper water tank in the form of a rectangular parallelepiped is to made. If its length is to be \(a\) times its breadth \(b\), how high should it be that for a given capacity it should cost as little as possible?

*Problems in Differential Calculus*, Byerly, 1895

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The answer is: the height should be \(\dfrac{ab}{a+1}\) if the tank is open, and \(\dfrac{2ab}{a+1}\) if the tank is closed