(So i was trying to find how to allocate my stats in my rpg character and i stumble across something i don't know how to formulate):
Maximize $$Z = \frac{x_1}{100}*\left(1+\frac{x_2}{100}\right)*(bd+0.5*x_1) + \left(1-\frac{x_1}{100}\right)*(bd+0.5*x_1)$$ ($bd$ is constant) subject to:
$$x_1 \geq 41$$ $$x_2 \geq 40$$ $$x_1 + x_2 \leq 2000$$ $$x_j \geq 0$$ $$x_1, x_2 \text{integer}$$
$\frac{x_1}{100}$ in the first term of objective function represent a probability and $\left(1-\frac{x_1}{100}\right)$ the complement.
My problem is that when $x_1>100$ i want my objective function to take account only the first term $$\left(1+\frac{x_2}{100}\right)*(bd+0.5*x_1)$$ with $\frac{x_1}{100}=1$ (so the second term isn't considered $\left(1-\frac{x_1}{100}\right)=0$). I thought of using integer variables but i don't know how to formulate the model. (I solved it in excel with if function but i want to know the analytic version)
(Background: $x_1$ points of stat 1 (Dexterity) and in this game it contributes to critical chance and damage, where as $x_2$ (Cunning) contributes to critical damage)
If there is another way to formulate, i'll be glad to see it.
Thank you for your time.