How to minimize $|Ax+By + C|$ given that $x \geq 0$ and $y\geq 0$

Question

I am trying to solve problem related to absolute value function, i.e given $Z(x,y) = |Ax + By + C|$ , what is the minimum value of $Z$, if $x \geq 0$ and $y\geq 0$ and x,y belongs to integers

Answer 1

The absolute value is always $\ge0$.
In this case, if there is no restriction on the value of A, B, or C, then $x=y=0$ and $C=0$ will make $Z=0$, which is the smallest you can get for an absolute value.