数学实验_08_1317417045吴张伟

1、数学实验实 验 报 告08实验名称 线性规划 实验日期2016.04.28 班级 13信计 学号 1317417045 姓名 吴张伟 成绩 一、实验目的（1）掌握用MATLAB优化工具箱和LINGO解线性规划的方法；（2）练习建立实际问题的线性规划模型.二、实验内容大学数学实验实验8后面的第8题（用MATLAB的linprog和LINGO分别实现，其中LINGO实现要求用简单编程和集合生成器分别编程实现；并且要求模仿实验8食谱问题例子那样进行敏感性分析，自问自答）。三、实验结果（包括所用命令、程序，运行结果等）（1）c = 1.80, 3.50, 0.40, 1.00;A = 0.5 1.0

2、2.0 6.0 2.0 4.0 0.5 1.0 5.0 2.0 1.0 2.5;b = 40.0, 20.0, 45.0;v = 0 0 0 0 ;x,z0,ef,out,lag = linprog(c,-A,-b,v,) lag.ineqlin, lag.lower Optimization terminated successfully.x = 5.0000 0.0000 20.0000 0.0000z0 = 17.0000ef = 1out = iterations: 10 cgiterations: 0 algorithm: 'lipsol'lag = ineqlin:

3、 3x1 double eqlin: 0x1 double upper: 4x1 double lower: 4x1 doubleans = 0.0000 0.4000 0.2000ans = 0.0000 1.5000 0.00000.1000即每天吃5磅干草和20磅高蛋白浓缩料，最小成本为17美元。对蛋白质的需求提高一个单位，成本不改变。（2）min = 1.8*x1+3.5*x2+0.4*x3+1*x4;0.5*x1 + 1*x2+ 2*x3+ 6*x4 >40;2*x1 + 4*x2+ 0.5*x3+ 1*x4 >20;5*x1+ 2*x2 + 1*x3+ 2.5*x4 &

4、gt;45; Global optimal solution found. Objective value: 17.00000 Infeasibilities: 0.000000 Total solver iterations: 4 Variable Value Reduced Cost X1 5.000000 0.000000 X2 0.000000 1.500000 X3 20.00000 0.000000 X4 0.000000 0.1000000 Row Slack or Surplus Dual Price 1 17.00000 -1.000000 2 2.500000 0.0000

5、00 3 0.000000 -0.4000000 4 0.000000 -0.2000000变程：Ranges in which the basis is unchanged: Objective Coefficient Ranges Current Allowable Allowable Variable Coefficient Increase Decrease X1 1.800000 0.2000000 0.2000000 X2 3.500000 INFINITY 1.500000 X3 0.4000000 0.4687500E-01 0.4000000E-01 X4 1.000000

6、INFINITY 0.1000000 Righthand Side Ranges Row Current Allowable Allowable RHS Increase Decrease 2 40.00000 2.500000 INFINITY 3 20.00000 2.500000 0.1315789 4 45.00000 0.3333333 5.000000（3）MODEL:sets: sn/1.4/:c,x; sm/1.3/:b; link(sm,sn):A;endsetsdata: c=1.8, 3.5, 0.4, 1; A=0.5 1 2 6 2 4 0.5 1 5 2 1 2.5

7、 ; b=40,20,45;enddataobj min = sum(sn:c*x);for(sm(i): constraintssum(sn(j):A(i,j)*x(j)>b(i););END Global optimal solution found. Objective value: 17.00000 Infeasibilities: 0.000000 Total solver iterations: 4 Variable Value Reduced Cost C( 1) 1.800000 0.000000 C( 2) 3.500000 0.000000 C( 3) 0.40000

8、00 0.000000 C( 4) 1.000000 0.000000 X( 1) 5.000000 0.000000 X( 2) 0.000000 1.500000 X( 3) 20.00000 0.000000 X( 4) 0.000000 0.1000000 B( 1) 40.00000 0.000000 B( 2) 20.00000 0.000000 B( 3) 45.00000 0.000000 A( 1, 1) 0.5000000 0.000000 A( 1, 2) 1.000000 0.000000 A( 1, 3) 2.000000 0.000000 A( 1, 4) 6.00

9、0000 0.000000 A( 2, 1) 2.000000 0.000000 A( 2, 2) 4.000000 0.000000 A( 2, 3) 0.5000000 0.000000 A( 2, 4) 1.000000 0.000000 A( 3, 1) 5.000000 0.000000 A( 3, 2) 2.000000 0.000000 A( 3, 3) 1.000000 0.000000 A( 3, 4) 2.500000 0.000000 Row Slack or Surplus Dual Price OBJ 17.00000 -1.000000 CONSTRAINTS( 1

10、) 2.500000 0.000000 CONSTRAINTS( 2) 0.000000 -0.4000000 CONSTRAINTS( 3) 0.000000 -0.2000000变程：Ranges in which the basis is unchanged: Objective Coefficient Ranges Current Allowable Allowable Variable Coefficient Increase Decrease X( 1) 1.800000 0.2000000 0.2000000 X( 2) 3.500000 INFINITY 1.500000 X( 3) 0.4000000 0.4687500E-01 0.4000000E-01 X( 4) 1.000000 INFINITY 0.1000000 Righthand Side Ranges Row Current Allowable Allowable RHS Increase Decrease CONSTRAINTS( 1) 40.00000 2.500000 INFINITY CONSTRAINTS( 2) 20