Find two positive numbers satisfying the given requirements.

Question

The sum of the first and twice the second is 160 and the product is a maximum.

first value:

second value:

Answer 1

x + 2y = 160

Product P = xy

x = 160 - 2y

then P = (160-2y)y = 160y - 2y²

Take the derivative of P set to 0

P' = 160 - 4y = 0

y = 40, and x = 4