-Find two positive numbers satisfying the given requirements:

Question

The sum of the first and twice the second is 80 and the product is a maximum.

Answer 1

a +2 b = 80 so a = 80 - 2 b
y = a b so y = (80-2 b)b = 80 b - 2 b^2
dy/db = 80 - 4 b
= 0 for max or min
4 b = 80
b = 20
then a = 40