用MATLB求解问题过程

1、实验一、第四章例题求解过程实验序号：1日期：2012年4月17日班级数学学院2009级C班学号094080185实验名称例题求解过程（课堂练习）问题的背景:'掌握matlab中的一些基本命令的使用是后面的实验和今后实际工作所必须的；实验目的和容: 例1奶制品问题（1）例2奶制品问题（2）例3自来水输送第一问模型第二问模型（书上的模型）第二问模型（正确的模型）例4货机装运例5汽车厂生产计划第1问模型第2问 有产量限制，要么不生产，要么至少生产80辆模型1混合线性规划模型（取 M足够大，例如 M=250）第2问模型2非线性规划模型例6原油采购与加工 模型一非线性规划模型模型二线性规划模型例

2、7选课策略模型1选课门数最少模型2选课门数最少，学分最多实验所用软件及版本：Matlab LINGO实验过程：例1奶制品问题（1）>> c=-72-64;>> A=1 1;128;3 0;>> b=50;480;100;>> aeq=;>> beq=;>> vlb=0;0;>> vub=;>> x,favl=li nprog（c,A,b,aeq,beq,vlb,vub） Optimization terminated.x =20.000030.0000favl =-3.3600e+003>&g

3、t;例2奶制品问题（2）>> c=-24 -16 -44 -32 3 3;>> A=1/3 1/4 0 0 1/3 1/4;4 2 0 0 6 4;>> b=50;480;>> aeq=0 0 1 0 -0.8 0;0 0 0 1 0 -0.75;>> beq=O;O;>> vlb=O;O;O;O;O;O;O;>> vub=;>> x,fval=li nprog(c,A,b,aeq,beq,vlb,vub)Warning: Len gth of lower bou nds is > len g

4、th(x); ignoring extra bou nds.> In checkbou nds at 27In linprog at 187Optimization terminated.x =0.0000168.000019.20000.000024.00000.0000fval =-3.4608e+003>>例3自来水输送第一问模型model:min =160*x11 + 130*x12+220*x13+170*x14+140*x21 + 130*x22+190*x23+150*x24+190*x31+200*x32+230*x33; x11+x12+x13+x14=50

5、;x21+x22+x23+x24=60;x31+x32+33=50;x11+x21+x31>=30;x11+x21+x31<=80;x12+x22+x32>=70;x12+x22+x32<=140;x13+x23+x33>=10;x13+x23+x33<=30;x14+x24>=10;x14+x24<=50;end modelGlobal optimal soluti on found at iterati on:0Objective value:18460.00VariableValueReduced CostX110.00000020.000

6、00X1250.000000.000000X130.00000030.00000X140.00000020.00000X2113.000000.000000X2227.000000.000000X2310.000000.000000X2410.000000.000000X3117.000000.000000X320.00000020.00000X330.000000170.0000RowSlack or SurplusDual Price118460.00-1.00000020.000000-130.000030.000000-130.000040.000000-180.000050.0000

7、00-10.00000650.000000.00000077.0000000.000000863.000000.00000090.000000-60.000001020.000000.000000110.000000-20.000001240.000000.000000第二问模型（书上的模型）model:min =160*x11+130*x12+220*x13+170*x14+140*x21 + 130*x22+190*x23+150*x24+190*x31+200*x32+230*x33;x11+x12+x13+x14<=100;x21+x22+x23+x24<=120;x31+

8、x32+x33<=100;x11+x21+x31>=30;x11+x21+x31<=80;x12+x22+x32>=70;x12+x22+x32<=140;x13+x23+x33>=10;x13+x23+x33<=30;x14+x24>=10;x14+x24<=50;end modelGlobal optimal soluti on found at iterati on:4VariableValueReduced CostX110.00000020.00000X120.0000000.000000X130.00000030.00000X1

9、40.00000020.00000X2130.000000.000000X2270.000000.000000X2310.000000.000000X2410.000000.000000X310.00000050.00000X320.00000070.00000X330.00000040.00000RowSlack or SurplusDual Price116700.00-1.0000002100.00000.00000030.0000000.0000004100.00000.00000050.000000-140.0000650.000000.00000070.000000-130.000

10、0870.000000.00000090.000000-190.00001020.000000.000000110.000000-150.00001240.000000.000000Objective value:16700.00第二问模型（正确的模型）model:min =160*x11+130*x12+220*x13+170*x14+140*x21 + 130*x22+190*x23+150*x24+190*x31+200*x32+230*x33;x11+x12+x13+x14<=100;x21+x22+x23+x24<=120;x31+x32+x33<=100;x11+

11、x21+x31=80;x12+x22+x32=140;x13+x23+x33=30;x14+x24=50;end modelGlobal optimal solution found at iteration:Objective value:646300.00VariableValueReduced CostX110.00000020.00000X12100.00000.000000X130.00000040.00000X140.00000020.00000X2130.000000.000000X2240.000000.000000X230.00000010.00000X2450.000000

12、.000000X3150.000000.000000X320.00000020.00000X3330.000000.000000RowSlack or SurplusDual Price146300.00-1.00000020.00000050.0000030.00000050.00000420.000000.00000050.000000-190.000060.000000-180.000070.000000-230.000080.000000-200.0000例4货机装运model:max=3100*(x11+x12+x13)+3800*(x21+x22+x23)+3500*(x31+x3

13、2+x33)+2850*(x41+x42+x43);x11+x21+x31+x41<=10;x12+x22+x32+x42<=16;x13+x23+x33+x43<=8;480*x11+650*x21+580*x31+390*x41<=6800;480*x12+650*x22+580*x32+390*x42<=8700;480*x13+650*x23+580*x33+390*x43<=5300;(x11+x21+x31+x41)/10=(x12+x22+x32+x42)/16;(x12+x22+x32+x42)/16=(x13+x23+x33+x43)/8;

14、x11+x12+x13<=18;x21+x22+x23<=15;x41+x42+x43+x43<=12;end modelGlobal optimal soluti on found at iterati on:0Objective value:121515.8VariableValueReduced CostX110.000000400.0000X120.00000057.89474X130.000000400.0000X217.0000000.000000X220.000000239.4737X238.0000000.000000X313.0000000.000000X3

15、212.947370.000000X330.0000000.000000X410.000000650.0000X423.0526320.000000X430.000000650.0000RowSlack or SurplusDual Price1121515.81.00000020.0000000.00000030.0000005453.28940.0000000.0000005510.00000.00000060.0000003.4210537100.00000.00000080.00000035000.0090.000000-28000.001018.000000.000000110.000000300.0000128.9473680.000000例5汽车厂生产计划第1model:max=2*x1+3*x2+4*x3;280*x1+250*x2+400*x3<=600