江西财经大学 0405学年第二学期期末考试试卷 试卷代码:03883B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 (a)When the simplex method solves for the next BF solution, elementary algebraic operations are used to eliminate each nonbasic variable from all but one equation (its equation) and to give it a coefficient of +1 in that one equation. (b) If a feasible solution is optimal but not a CPF solution, then infinitely many optimal solutions exist. ( (c) The simplex methods rule for choosing the entering basic variable is used because it always leads to the best adjacent BF solution(largest z).( ( d) The simplex methods minimum ratio rule fro choosing the leaving basic variable used because making another choice with a large ratio would yield a basic solution that is not feasible. (e)If at least one of the basic variables has a coefficient of zero in row o of the final tableau, then the problem has multiple optimal solutions. 2. A company needs to lease warehouse storage space over the next 5 months. Just how much space will be required in each of these months is known. However, since these space requirements are quite different, it may be most economical to lease only the amount needed each month on a month-by-month basis. On the other hand, the additional cost for leasing space for additional months is much less than for the first month, so it may be less expensive to lease the maximum amount needed for the entire 5 months. Another option is the intermediate approach of changing the total amount of space leased(by adding a new lease and /or having an old lease expire)at least once but not every month The space requirement (in thousands of square feet) and the leasing costs(in hundreds of dollars) for the various leasing periods are as follows month Required space (000Leasing eriod Cost per 1,000 square Square feet) (Months) feet leased ($00 650 12345 20 1.000 350 600 The objective is to minimize the total leasing cost for meeting the space requirements. Please 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：03883B 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) When the simplex method solves for the next BF solution, elementary algebraic operations are used to eliminate each nonbasic variable from all but one equation (its equation) and to give it a coefficient of +1 in that one equation. ( ) (b) If a feasible solution is optimal but not a CPF solution, then infinitely many optimal solutions exist. ( ) (c) The simplex method’s rule for choosing the entering basic variable is used because it always leads to the best adjacent BF solution (largest Z).( ) (d) The simplex method’s minimum ratio rule fro choosing the leaving basic variable is used because making another choice with a large ratio would yield a basic solution that is not feasible.( ) (e) If at least one of the basic variables has a coefficient of zero in row 0 of the final tableau, then the problem has multiple optimal solutions. ( ). 2. A company needs to lease warehouse storage space over the next 5 months. Just how much space will be required in each of these months is known. However, since these space requirements are quite different, it may be most economical to lease only the amount needed each month on a month-by-month basis. On the other hand, the additional cost for leasing space for additional months is much less than for the first month, so it may be less expensive to lease the maximum amount needed for the entire 5 months. Another option is the intermediate approach of changing the total amount of space leased (by adding a new lease and /or having an old lease expire) at least once but not every month. The space requirement (in thousands of square feet) and the leasing costs (in hundreds of dollars) for the various leasing periods are as follows: Month Required space (000 Square feet) Leasing period (Months) Cost per 1,000 square feet leased ($00) 1 30 1 650 2 20 2 1,000 3 40 3 1,350 4 10 4 1,600 5 50 5 1,900 The objective is to minimize the total leasing cost for meeting the space requirements. Please formulate a linear programming model for this problem. (10 points)