But I think its use is totally unnecessary here. In fact, you don't even have to add any artificial variables. Here's LP formulation that I've used in my simplex solution:

Code: Select all

```
minimize (A+B+C) - \sum_{i=1}^n (a[i] + b[i] + c[i]) x[i]
subject to
\sum_{i=1}^n a[i] x[i] <= A
\sum_{i=1}^n b[i] x[i] <= B
\sum_{i=1}^n c[i] x[i] <= C
x[i] >= 0
```