Find two positive numbers such that the sum of the first and twice the second is 100 and their product is a maximum.

Answer 1

let the two numbers be x and y
x + 2y = 100

product = xy
= (100-2y)(y)
= 100y - 2y^2
d(product)/dy = 100 - 4y
= 0

4y = 100
y = 25
x = 100 - 50 = 50

they are 25 and 50