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Find two numbers whose sum is 16 and whose product is a maximum.

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Two numbers whose sum is 16 and whose product is a maximum have to be determined. Let one of the numbers be X, the other number is (16 - X)

The product of the numbers is P = X*(16 - X) = 16X - X^2

To maximize the product solve P' = 0

=> 16 - 2X = 0

=> X = 8

The two numbers are 8 and 8

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