江西财经大学 05-06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:04管理科学专业 1. Fill in the blanks (10 points) (a)the four assumptions of linear programming are ①②③④ (b)the difference between simplex method and dual simplex method are: (c)the duality theorem stated that the only possible relationship between the primal and the dual problems are ①②③ 2. We want to select an advertising strategy to reach two types of customers homemakers in families with over $25,000 annual income and homemakers in families with under $25,000 income. We feel that people in the first group will purchase twice as much of our product as people in the second, and our goal is to maximize purchases. We may advertise either on TV or in a magazine; one unit ofT advertising costs $40,000 and reaches approximately 20,000 people in the first group and 80,000 in the second. One unit of advertising in the magazine costs $24,000 and reaches 60,000 people in the first group and 30,000 in the second We require that at least 6 units of Tv advertising be used and that no more than 12 units of magazine advertising be used for policy reasons. The advertising budget is 360,000 Formulate this problem as a linear programming problem, defining all variables used.(10 points) 3.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 ducts 1, 2, and 3. The available capacity on the machines that might limit output is summarized in the following table1 江西财经大学 05-06 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：04 管理科学专业 1.Fill in the blanks. (10 points) (a) the four assumptions of linear programming are: ① ; ② ; ③ ④ 。 (b) the difference between simplex method and dual simplex method are: ① ; ② ③ . (c) the duality theorem stated that the only possible relationship between the primal and the dual problems are: ① . ② . ③ . 2.We want to select an advertising strategy to reach two types of customers: homemakers in families with over $25,000 annual income and homemakers in families with under $25,000 income. We feel that people in the first group will purchase twice as much of our product as people in the second, and our goal is to maximize purchases. We may advertise either on TV or in a magazine; one unit of TV advertising costs $40,000 and reaches approximately 20,000 people in the first group and 80,000 in the second. One unit of advertising in the magazine costs $24,000 and reaches 60,000 people in the first group and 30,000 in the second. We require that at least 6 units of TV advertising be used and that no more than 12 units of magazine advertising be used for policy reasons. The advertising budget is 360,000. Formulate this problem as a linear programming problem, defining all variables used. (10 points) 3.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: