This method is another method to solve a given L.P.P. involving some artificial variable. In this method solution is obtained in two phases.
Phase-I
In this phase, we construct an auxiliary L.P.P. leading to a final simplex table. Various steps are given below:
(1) Assign cost – 1 to each artificial variable and cost 0 to all other variables. Also find a new objective function Z*.
(2) Solve the auxiliary L.P.P by simplex method until either following two cases arise.
(i) Max Z* < 0 and at least one artificial variable appears in the optimum basis at positive level. In this case L.P.P. dose not possess any feasible solution.
(ii) Max Z* = 0 and at least one artificial variable or no artificial variable appears in optimum basis. In both the cases, we go to the phase II.
Phase-II
Use solution of phase 1 as the initial value of phase-II. Assign the actual cost to the variables and zero cost of every artificial variable. Delete the artificial variable column from the table. Apply simplex method to the modified simplex table to find the solution.
