实验一_线性规划模型及应用.docx

实验一线性规划模型及应用一、实验学时：2学时二、实验类型：综合性三、实验目的和主要内容：目的：1. 练习建立实际问题的线性规划模型2. 掌握用LINDO软件求解线性规划问题主要内容：1.某化工厂要用三种原材料C、P、H混合配出三种不同规格的产品A、B、D已知产品的规格要求，产品单价，每天能供应的原材料数量及原材料单价如表1所示，求最优生产计划表1产品的规格要求，产品单价、原材料数量及原材料单价原料产品ABC供应量（kg/天）单价（元/kg）C>50%>25%10065P10025H<25%<50%6035单价（元/kg）5035252. 连续投资问题某部门在今后五年内考虑给下列项目投资，已知：项目A，从第一年到第四年年初需要投资，并于次年末回收本利110%；项目B，第三年初需要投资，到第五年末能回收本利115%，但规定最大投资额不超过4万元;项目C，第二年初需要投资，到第五年末能回收本利130%，但规定最大投资额不超过3万元;项目D，五年内每年初可购买公债，于当年末归还，并加利息3%该部门现有资金10万元，问它应如何确定给这些项目每年的投资额，使到第五年末拥有资金的本利总额为最大？四、实验仪器设备和材料：微机和LINDO及LINGO软件五、实验过程命令max25yl+10y2+15zl-15xl-30x2-40x3-10z3stxl+x2+x3v=100yl+y2+y3v=100z1+z2+z3<=60x1-y1-z1>=03y1-x1-z1<=03x2-y2-z2>=0y2-x2-z2<=03x3-y3-z3>=0y3-x3-z3<=0end运行结果：LPOPTIMUMFOUNDATSTEP5OBJECTIVEFUNCTIONVALUE1)500.0000VARIABLEVALUEREDUCEDCOSTY150.0000000.000000Y20.0000000.000000Z150.0000000.000000X1100.0000000.000000X20.00000015.000000X30.00000045.000000Z30.00000010.000000Y30.0000000.000000Z20.0000000.000000ROWSLACKORSURPLUSDUALPRICES2)0.0000005.0000003)50.0000000.0000004)10.0000000.0000005)0.000000-17.5000006)0.0000002.5000007)0.000000-5.0000008)0.0000005.0000009)0.0000000.00000010)0.0000000.000000NO.ITERATIONS=5RANGESINWHICHTHEBASISISUNCHANGED:OBJCOEFFICIENTRANGESVARIABLECURRENTALLOWABLEALLOWABLECOEFY125.000000Y210.000000Z115.000000X1-15.000000X2-30.000000X3-40.000000Z3-10.000000Y30.000000Z20.000000INCREASEINFINITY7.50000010.000000INFINITY15.00000045.00000010.0000000.00000010.000000DECREASE10.00000010.00000010.0000005.000000INFINITYINFINITYINFINITYINFINITY10.000000RIGHTHANDSIDERANGESROWCURRENTRHSALLOWABLEALLOWABLEINCREASEDECREASE2100.00000020.000000100.0000003100.000000INFINITY50.000000460.000000INFINITY10.00000050.00000066.66666413.33333360.000000200.00000040.00000070.0000000.00000020.00000080.0000000.0000000.00000090.0000000.000000INFINITY100.000000INFINITY0.000000命令：Max1.15b+1.3c+1.1a41+1.03d51sta11+d11<=10c+a21+d21+a11-0.03d11<=10b+a31+d31+a21-0.03d21-0.1a11+c<=10a41+d41+b+c+a31-0.03d31-0.1a21<=10d51+b+c+a41-0.03d41-0.1a31<=10b<=4c<=3end运行结果：LPOPTIMUMFOUNDATSTEP2OBJECTIVEFUNCTIONVALUE1)11.90510VARIABLEVALUEREDUCEDCOSTB4.0000000.000000C3.0000000.000000A410.0000000.024396D513.3059210.000000A116.5125710.000000D113.4874290.000000A210.5920520.000000D210.0000000.000577A313.0592050.000000D310.0000000.005772D410.0000000.063496ROWSLACKORSURPLUSDUALPRICES2)0.0000000.0000253)0.0000000.0008354)0.0000000.0086045)0.0000000.0943966)0.0000001.0300007)0.0000000.0170008)0.0000000.166165NO.ITERATIONS=2RANGESINWHICHTHEBASISISUNCHANGED:OBJCOEFFICIENTRANGESVARIABLECURRENTALLOWABLEALLOWABLECOEFINCREASEDECREASEB1.150000INFINITY0.017000C1.300000INFINITY0.166165A411.1000000.024396INFINITYD511.0300000.0154550.022348A110.0000000.0069100.000630D110.0000000.0006300.000026A210.0000000.0292040.006709D210.0000000.000577INFINITYA310.0000000.0170000.026619D310.0000000.005772INFINITYD410.0000000.063496INFINITYRIGHTHANDSIDERANGESROWCURRENTALLOWABLEALLOWABLERHSINCREASEDECREASE210.000000INFINITY310.0000003.909091410.0000008.030000510.0000000.708738610.000000INFINITY74.0000003.00538283.0000003.0031683.5833337.3000000.7087383.3380533.3059214.0000003.000000。