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algorithm allowable increase assignment problem BASIC COEFFICIENT basic feasible solution basic variables capacity cell column complete Consider constraint set contour corner solution critical path decision variables decrease demand dollars dual price equality constraint form equations example feasible region flow formulation graphical inequality constraint infeasible integer integer linear programming inventory label labor linear programming LP model LP problem LP relaxation marginal cost Max model maximize minimize minimum minimum spanning tree node nonbasic variables nondegenerate objective function objective value obtain opportunity cost optimal solution optimal value original problem plant portfolio pounds profit PROTRAC quantity real-world right-hand side route S₁ S₂ satisfy schedule Section sensitivity analysis shown in Figure simplex algorithm simplex method slack or surplus slack variable solve standard equality constraint supply surplus variables tomatoes transportation problem unit warehouse x₁ y₁ zero