I have 3x + y = 1100, the combination x samples out of 500 C(500, x) and the combination y samples out of 500 C(500, y).
I want to maximize C(500, x) * C(500, y).
Any one could you solve x, y using high school math? Thanks a lot!
A intuition would be letting x and y be as close as possible to 250 to max the combination. I got the formula to minimize (250 - x)^2 + (250 - y)^2 but I don't know if there is any theory supporting this.