I'm given an inequality $a_1x_1 + a_2x_2 \geq c_1$ where $a, c, x_1, x_2$ are integers and $x_1, x_2 \text{ are either } 1 \text{ or } 0$.
I'd like to construct another inequality $b_1y_1 + b_2y_2 \geq c_2$ where $b, c, y_1, y_2$ are integers in range $[-k, k]$ in a way s.t. first inequality is satisfiable iff second inequality is satisfiable.
I've tried to map $x_1, x_2$ to $y_1, y_2$ via affine transformation but it doesn't seem like the right approach.
How should I approach this problem?