Find two positive numbers where the sum of the first number and twice the second number is 108 and the product is a maximum.

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justaguide eNotes educator| Certified Educator

Two positive numbers have to be found where the sum of the first number and twice the second number is 108 and the product is a maximum.

Let one of the numbers be X, as the sum of the number and twice the second number is 108, the second number is (108 - X)/2

The product of the two numbers is P = 54X - X^2/2. To maximize P, solve for P' = 0

=> 54 - X = 0

=> X = 54

The second number is 27.

The two numbers are 54 and 27.