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.