When the primal-dual pairs’ objective values are equal, the solutions are optimal if the solutions are both feasible—neither of the solutions does violate their respective constraints. Put differently, a feasible solution of the primal solution (x) is not optimal if the dual solution (y) violates a constraint of the dual model. The simplex method concurrently identifies basic feasible solutions for a primal model and its dual. This is a property of the duality called complementary solutions property. This property allows checking for the optimality of the primal solution by inspecting the feasibility of its dual solution.