i want write a module to find the integer combination for a multi variable fomula. For example
$8x + 9y \le 124$
The module will return all possible positive integer for $x$ and $y$.Eg. $x=2$, $y=12$. It does not necessary be exactly $124$, could be any number less or equal to $124$. Must be as close as possible to $124$ if no exact solution could be found.
I do not want to solve with brute force as the number of variable could be any...$(5,10,100,...n)$
Any algorithm could solve this?