The function to be maximised is rewritten to include the sum of all the artificial variables.
3.
If the minimum is positive then there is no feasible solution for the Phase I problem where the artificial variables are all zero.
4.
If the minimum is 0 then the artificial variables can be eliminated from the resulting canonical tableau producing a canonical tableau equivalent to the original problem.
5.
Even if an optimal solution is not reached, the algorithm does produce one close to it, has an inherent polynomial-time test for optimality, as well as can be used as an excellent preprocessor that needs no artificial variable.
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