What is the largest possible product you can form from two non-negative numbers whose sum is 50? The maximum product is

Answer 1

2 numbers are x and y.

We are given x + y = 50, therefore y = 50 - x

product = p = x*y = x * (50 - x)

p = -x² + 50x

to find the maximum, take the first derivative and set = to 0:

p' = -2x + 50 = 0

x = 25

from the original equation, y is also 25.

CHECK:

25 * 25 = 625

24 * 26 = 26 * 24 = 624