I have an expression $$Ax+By+Cz.$$ where $A$, $B$ and $C$ are positive constants $\ge1$. The variables $x$, $y$ and $z$ are non-negative integers. I am also given a number $T$.
I want to find the largest integer value such that it is less than $T$ and not satisfied by $Ax+By+Cz$, how can I do it without using brute force.
I can use LinearProgramming but that will give me the value that is satisfied by $Ax+By+Cz$ such that it is less than T. But I want to find the largest value which is less than T, but doesn't belong to $Ax+By+Cz$ for any value of x, y and z