2. The Two Phase Simplex Method
Phase I: We create an artificial objective function as the sum of all
the artificial variables, and we minimize this objective function using
the tableau simplex method.
If the minimum value of this artificial objective function is zero, then
this means that all the artificial variables have been reduced to zero,
and we have a basic feasible solution to the original problem, and
we proceed to phase II. If this minimum value is positive, then this
means that the original problem is infeasible, so we terminate.
Phase II: The final tableau of phase I becomes the first tableau of
phase II using the original objective function now. Use the tableau
method again to obtain an optimal solution.