江西财经大学 03-04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:02管理科学专业 1. Label each of the following statements about linear programming problems as true or false (10 points) (a)For minimization problems, if the objective function evaluated at a CPF solution is no large than its value at every adjacent CPF solution, then that solution is optimal ( True (b)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. True (c) Only CPf solutions can be optimal, so the number of optimal solutions cannot exceed the number of CPF solutions( False (d)In a particular iteration of the simplex method, if there is a tie for which variable should be the leaving basic variable then the next bf solution must have at least one basic variable T (e) If there is no leaving basic variable at some iteration, then the problem has no feasibl solution.( False 2. You are the production manager for a manufacturer of three types of spare parts for automobiles. The manufacture of each part requires processing on each of two machines, with the following processing time(in hours ): (table 1) Table 1 Machine B 0.02 0.04 Each machine is available 40 hours per month. Each part manufactured will yield a unit profit as follows Part B Profit You want to determine the mix of spare parts to produce in order to maximize total profit Formulate a linear programming model for this problem. (10 points Solution: we set the mix of spare parts is xA, xB,xc The linear programming model1 江西财经大学 03-04 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：02 管理科学专业 1.Label each of the following statements about linear programming problems as true or false. (10 points) (a) For minimization problems, if the objective function evaluated at a CPF solution is no large than its value at every adjacent CPF solution, then that solution is optimal. ( True ). (b) 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. ( True ). (c) Only CPF solutions can be optimal, so the number of optimal solutions cannot exceed the number of CPF solutions. ( False ). (d) In a particular iteration of the simplex method, if there is a tie for which variable should be the leaving basic variable, then the next BF solution must have at least one basic variable equal to zero.( True ) (e) If there is no leaving basic variable at some iteration, then the problem has no feasible solution. ( False ). 2.You are the production manager for a manufacturer of three types of spare parts for automobiles. The manufacture of each part requires processing on each of two machines, with the following processing time (in hours):(table 1) Table 1 Part Machine A B C 1 0.02 0.03 0.05 2 0.05 0.02 0.04 Each machine is available 40 hours per month. Each part manufactured will yield a unit profit as follows: Part A B C Profit 50 40 30 You want to determine the mix of spare parts to produce in order to maximize total profit. Formulate a linear programming model for this problem.（10 points） Solution: we set the mix of spare parts is xA,xB,xC The linear programming model is