江西财经大学 05-06学年第二学期期末考试试卷(参考答案 试卷代码:03883A卷 课时 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 O Proportionality assumption: ② Addit ③ Divisible ④ Certainty assumption (b)the difference between simplex method and dual simplex method are the simplex method first to determine the entering basic variable, but dual simplex method first to determine leaving basic variable 2the criterion of the simplex method determine optimal is CrB-A-c20,but the criterion of the simplex method determine optimal is B-b>0 3 In simplex method minimum ratio test is to pick out each coefficient in the pivot column that is strictly positive divide each of these coefficients into the right side entry for the same row; but in dual simplex method minimum ratio test is to pick out each coefficient in the pivot row that is strictly negative divide each of these coefficients into row(0) entry for the same row. (c) the duality theorem stated that the only possible relationship between the primal and the dual problems are Oif one problem has feasible solution and a bounded obiective function, then so do the other problem, so both the weak and strong duality properties are applicable. 2 if one problem has feasible solutions and an unbounded obiective function,then the other problem has no feasible solutions. 3 if one problem has no feasible solutions, then the other problem has either no feasible solutions or an unbounded obiective function. 2. We want to select an advertising strategy to reach two types of customers homemakers in families with over $25000 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 and1 江西财经大学 05-06 学年第二学期期末考试试卷（参考答案） 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 Proportionality assumption; ②Additivity assumption; ③ Divisible assumption; ④ Certainty assumption。 (b) the difference between simplex method and dual simplex method are: ① the simplex method first to determine the entering basic variable, but dual simplex method first to determine leaving basic variable; ②the criterion of the simplex method determine optimal is CB B A − C ≥ o −1 ,but the criterion of the simplex method determine optimal is 0 1 ≥ − B b ③ In simplex method minimum ratio test is to pick out each coefficient in the pivot column that is strictly positive divide each of these coefficients into the right side entry for the same row; but in dual simplex method minimum ratio test is to pick out each coefficient in the pivot row that is strictly negative divide each of these coefficients into row (0) entry for the same row. (c) the duality theorem stated that the only possible relationship between the primal and the dual problems are: ①if one problem has feasible solution and a bounded objective function, then so does the other problem, so both the weak and strong duality properties are applicable. ② if one problem has feasible solutions and an unbounded objective function, then the other problem has no feasible solutions. ③ if one problem has no feasible solutions, then the other problem has either no feasible solutions or an unbounded objective function. 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