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The Simplex Method
Duality and the Revised Simplex Method
3 other sections not shown
algorithm alternative optima artificial variables assignment problem asterisk basic feasible solution basic solution Basic Variables basis matrix become non-basic becomes basic choose column vector components contains convex set corresponding dual constraints dual problem dual simplex method dual variables elements ellipsoid ellipsoid method finite given Hence hyperplane inequality 5.1 integers iteration linear programming problem linearly independent matrix game maximizing problem minimizing Minimum cost non-basic variables non-degenerate non-negativity restrictions non-zero objective function obtain optimal basic feasible optimal dual tableau optimal mixed strategy optimal primal tableau optimal solution optimal tableau pay-off matrix perturbed primal problem problems 3.1 proof pure strategies revised simplex method saddle-point satisfied Section shadow price simplex calculations simplex rules simplex tableau simplex transformation slack variables solved standard simplex method sub-game Suppose surplus variables Tableau 1 Example Theorem transportation problem unbounded solution unbounded value unique variable Xj Zj-cj ZJ~cJ