2015北工大数学建模课程作业三

《2015北工大数学建模课程作业三》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、2015北工大数学建模课程作业三1.生产计划安排(1)设装配的玩具火车、玩具卡车和玩具汽车的数量分别为x,y,z用Lingo建立线性规划模型如下：x+2*y+z<=430;3*x+0+2*z<=460;x+4*y+0<=420;@gin(x);@gin(y);@gin(z);max=3*x+2*y+5*z;求解得到Globaloptimalsolutionfound.Objectivevalue:1350.000Objectivebound:1350.000Infeasibilities:0.000000Extendedsolverst

2、eps:0Totalsolveriterations:0Elapsedruntimeseconds:0.07ModelClass:PILPTotalvariables:3Nonlinearvariables:0Integervariables:3Totalconstraints:4Nonlinearconstraints:0Totalnonzeros:10Nonlinearnonzeros:0VariableValueReducedCostX0.000000-3.000000Y100.0000-2.000000Z230.0000-5.0

3、00000RowSlackorSurplusDualPrice10.0000000.00000020.0000000.000000320.000000.00000041350.0001.000000生产0辆玩具火车、100辆玩具卡车和230辆玩具起汽车时获利最多1350.00元，即为最优的生产方案。(2)由题意，去掉第一个约束并修改目标函数，模型如下：3*x+0+2*z<=460;x+4*y+0<=420;t=x+2*y+z-430;@gin(t);@gin(x);@gin(y);@gin(z);max=3*x+2*y+5*z-50*(

4、t)/60;求解得到Globaloptimalsolutionfound.Objectivevalue:1351.667Objectivebound:1351.667Infeasibilities:0.000000Extendedsolversteps:0Totalsolveriterations:2Elapsedruntimeseconds:0.06ModelClass:PILPTotalvariables:4Nonlinearvariables:0Integervariables:4Totalconstraints:4Nonline

5、arconstraints:0Totalnonzeros:12Nonlinearnonzeros:0VariableValueReducedCostX0.000000-3.000000Z230.0000-5.000000Y105.0000-2.000000T10.000000.8333333RowSlackorSurplusDualPrice10.0000000.00000020.0000000.00000030.0000000.00000041351.6671.000000即使用加班在经济上有利，最多加班T=10分钟，获利为1351.

6、67元。(3)2号操作员加班2小时相当于操作2的时间限制延长120分钟，即操作2的时间限制变为580分钟。修改模型如下：x+2*y+z<=430;3*x+0+2*z<=580;x+4*y+0<=420;@gin(x);@gin(y);@gin(z);max=3*x+2*y+5*z-(45+10)*2;求解得到Globaloptimalsolutionfound.Objectivevalue:1480.000Objectivebound:1480.000Infeasibilities:0.000000Extendedsolversteps

7、:0Totalsolveriterations:0Elapsedruntimeseconds:0.05ModelClass:PILPTotalvariables:3Nonlinearvariables:0Integervariables:3Totalconstraints:4Nonlinearconstraints:0Totalnonzeros:10Nonlinearnonzeros:0VariableValueReducedCostX0.000000-3.000000Y70.00000-2.000000Z290.0000-5.0000

8、00RowSlackorSurplusDualPrice10.0000000.00000020.0000000.0000003140.00000.00000041480.0001.000000这项活动使获利