calculus
A rectangular beam is cut from a cylindrical log of radius 25 cm. The strength of a beam of width w and height h is proportional to wh2. (See Figure 4.70.) Find the width and height of the beam of maximum strength.
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The width of the beam should be 25 cm and the height should be 1 cm. This is the maximum strength because with a width of 25 cm, all of the strength of the cylindrical log is being utilized and a height of 1 cm will maximize the strength as the height to width ratio is greater, meaning the ratio of width to height squared is greater and thus the strength is greater.
