58 - 59 Maxima and minima: cylinder surmounted by hemisphere and cylinder surmounted by cone

Problem 58
For the silo of Problem 57, find the most economical proportions, if the floor is twice as expensive as the walls, per unit area, and the roof is three times as expensive as the walls, per unit area.

56 - 57 Maxima and minima problems of square box and silo

Problem 56
The base of a covered box is a square. The bottom and back are made of pine, the remainder of oak. If oak is m times as expensive as pine, find the most economical proportion.

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