Here is the inequality: $a\_{1}x\_{1}+a\_{2}x\_{2}+\dots+a\_{n}x\_{n} \leq B$. 
Assume we know the values of $\{a\_{1},a\_{2},\dots,a\_{n}\}$ ($a\_{i} > 0, \forall i \in [1,n]$)and $B$, is there any algorithm that can be used to quickly find a solution of $\{x\_{1},x\_{2},\dots,x\_{n}\}$, given that $x\_i$ is an integer and $x\_{i} \geq 0 $ ($\forall i \in [1,n]$)? I want the solution to make $a\_{1}x\_{1}+a\_{2}x\_{2}+\dots+a\_{n}x\_{n}$ approximate $B$ as closely as possible.