江西财经大学 0405学年第二学期期末考试试卷 试卷代码:03883A卷 课时:64 课程名称:运筹学I(英) 适用对象:03管理科学专业 1. Label each of the following statements about linear programming problems as true or false(10 points) (a) The sum of the number of functional constraints and the number of variables (before augmenting) is the same for both the primal and the dual problems (b)At each iteration, the simplex method simultaneously identifies a CPF solution for the primal problem and a CPF solution for the dual problem such that their objective function values are the same. (c)If the value of the objective function is equal at two different feasible points X* and X*, then all points on the line segment connecting X and X** are feasible and z has the same value at all those points. (d)Only CPF solutions can be optimal, so the number of optimal solutions cannot exceed the number of cpf solutions (e) The dual simplex method is always used to solve the dual programming. 2.A manufacturing firm has discontinued the production of a certain unprofitable product line. This act created considerable excess production capacity. Management is considering devoting this excess capacity to one or more of three products; call them products 1, 2, and 3. The available capacity on the machines that might limit output is summarized in the following table Machine Type Available Time(in Machine Hours per Week) Milling machine 500 Lathe 350 150 The number of machine hours required for each unit of the respective products is as Machine Ty Product 1 Product 2 Product Lathe Grindel 2 The sales department indicates that the sales potential for products 1 and 2 exceeds the maximum production rate and that the sales potential for product 3 is 20 units per week. The unit profit would be $50, $20, and $25, respectively, on products 1, 2 and 3 the objective is to determine how much of each product the firm should produce to maximize profit Formulate a linear programming model for this problem. (10 points)1 江西财经大学 04-05 学年第二学期期末考试试卷 试卷代码：03883A 卷 课时：64 课程名称：运筹学 I（英） 适用对象：03 管理科学专业 1.Label each of the following statements about linear programming problems as true or false. (10 points) (a) The sum of the number of functional constraints and the number of variables (before augmenting) is the same for both the primal and the dual problems. ( ). (b) At each iteration, the simplex method simultaneously identifies a CPF solution for the primal problem and a CPF solution for the dual problem such that their objective function values are the same. ( ) (c) If the value of the objective function is equal at two different feasible points X* and X**, then all points on the line segment connecting X* and X** are feasible and Z has the same value at all those points. ( ). (d) Only CPF solutions can be optimal, so the number of optimal solutions cannot exceed the number of CPF solutions. ( ). (e) The dual simplex method is always used to solve the dual programming.( ) 2.A manufacturing firm has discontinued the production of a certain unprofitable product line. This act created considerable excess production capacity. Management is considering devoting this excess capacity to one or more of three products; call them products 1,2, and 3. The available capacity on the machines that might limit output is summarized in the following table: Machine Type Available Time (in Machine Hours per Week) Milling machine Lathe Grinder 500 350 150 The number of machine hours required for each unit of the respective products is as follows: Machine Type Product 1 Product 2 Product 3 Milling machine Lathe Grinder 9 5 3 3 4 0 5 0 2 The sales department indicates that the sales potential for products 1 and 2 exceeds the maximum production rate and that the sales potential for product 3 is 20 units per week. The unit profit would be $50, $20, and $25, respectively, on products 1,2 and 3. the objective is to determine how much of each product the firm should produce to maximize profit. Formulate a linear programming model for this problem. (10 points)