ABSTRACT
Simplex algorithm (a step by step or iterative approach) was originally proposed by G. B Dantzig in 1948. It starts at a basic (the worst case) level of the problem. At each step it projects the improvement in the objective function over its previous step. Thus, the solution becomes optimum when no further improvement is possible on the objective function. When the objective function is parallel to one of the constraints, the multiple optimal solutions may exist. The optimal solution exists at the extreme point on the feasible region, and the multiple optimal solutions will be noticed on at least two points of the binding constraint parallel to that of objective function. Thus in simplex method at least two solutions can be found. The objective function is split into two sub-objectives, one with artificial variables (and slack if any) only, while the second with the decision variables. Usually a Linear Programming Problem is assumed to have non-negative condition of variables.
