I have two binary variables $x_1$ and $x_2$ and a non-negative continuous variable $y$. In addition, I have the following two parameters $u>q>0$. I would like to formulate the following implications
- $x_1=0 \implies y=0$
- $(x_1,x_2)=(1,0) \implies y\leq u-q$
- $(x_1,x_2)=(1,1) \implies y\leq u$
I have managed to formulate these relations using the following two inequalities \begin{align} &y\leq ux_1\\ &y\leq (u-q)x_1 + qx_2 \end{align} However, I am wondering whether it can be achieved using only one inequality?