Introduction Definition 1.2 The feasible region for an LP is the set of all points that satisfies all the LP's constraints and sign restrictions.Any point that is not in an LP's feasible region is said to be an infeasible point. Definition 1.3 For a maximization problem,an optimal solution to an LP is a point in the feasible region with the largest objective function value.Similarly,for a minimization problem,an optimal solution is a point in the feasible region with the smallest objective function value. o Most LPs have only one optimal solution. Some LPs have no optimal solution. o Some LPs have an infinite number of solutions. Xi Chen (chenxi0109@bfsu.edu.cn) Linear Programming 7/148Introduction Definition 1.2 The feasible region for an LP is the set of all points that satisfies all the LP’s constraints and sign restrictions. Any point that is not in an LP’s feasible region is said to be an infeasible point. Definition 1.3 For a maximization problem, an optimal solution to an LP is a point in the feasible region with the largest objective function value. Similarly, for a minimization problem, an optimal solution is a point in the feasible region with the smallest objective function value. Most LPs have only one optimal solution. Some LPs have no optimal solution. Some LPs have an infinite number of solutions. Xi Chen (chenxi0109@bfsu.edu.cn) Linear Programming 7 / 148