中南统计专业运筹学作业.docx
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中南统计专业运筹学作业
运筹学作业
1.1
min=2*x1+3*x2;
4*x1+6*x2>=6;
3*x1+2*x2>=4;
Globaloptimalsolutionfound.
Objectivevalue:
3.000000
Infeasibilities:
0.000000
Totalsolveriterations:
2
ModelClass:
LP
Totalvariables:
2
Nonlinearvariables:
0
Integervariables:
0
Totalconstraints:
3
Nonlinearconstraints:
0
Totalnonzeros:
6
Nonlinearnonzeros:
0
VariableValueReducedCost
X11.2000000.000000
X20.20000000.000000
RowSlackorSurplusDualPrice
max=3*x1+2*x2;
2*x1+x2<=2;
3*x1+4*x2>=12;
Nofeasiblesolutionfound.
Infeasibilities:
4.000000
Totalsolveriterations:
1
ModelClass:
LP
Totalvariables:
2
Nonlinearvariables:
0
Integervariables:
0
Totalconstraints:
3
Nonlinearconstraints:
0
Totalnonzeros:
6
Nonlinearnonzeros:
0
VariableValueReducedCost
X10.0000001.000000
X22.0000000.000000
RowSlackorSurplusDualPrice
12.0000001.000000
20.0000002.000000
3-4.0000000.000000
max=x1+x2;
6*x1+10*x2<=120;
x1>=5;x1<=10;
x2>=3;x2<=8;
Globaloptimalsolutionfound.
Objectivevalue:
16.00000
Infeasibilities:
0.000000
Totalsolveriterations:
1
ModelClass:
LP
Totalvariables:
2
Nonlinearvariables:
0
Integervariables:
0
Totalconstraints:
6
Nonlinearconstraints:
0
Totalnonzeros:
8
Nonlinearnonzeros:
0
VariableValueReducedCost
X110.000000.000000
X26.0000000.000000
RowSlackorSurplusDualPrice
116.000001.000000
20.0000000.1000000
35.0000000.000000
40.0000000.4000000
53.0000000.000000
62.0000000.000000
max=5*x1+6*x2;
2*x1-x2>=2;
-2*x1+3*x2<=2;
Modelisunbounded
ModelClass:
LP
Totalvariables:
2
Nonlinearvariables:
0
Integervariables:
0
Totalconstraints:
3
Nonlinearconstraints:
0
Totalnonzeros:
6
Nonlinearnonzeros:
0
VariableValueReducedCost
X12.0000000.000000
X22.0000000.000000
RowSlackorSurplusDualPrice
1-0.1000000E+311.000000
20.0000006.750000
30.0000004.250000
1.2
min=-3*x1+4*x2-2*x3+5*x4;
4*x1-x2+2*x2-x4=-2;
x1+x2-x3+2*x4<=14;
-2*x1+3*x2+x3-x4>=2;
end
freex4;
Modelisunbounded
ModelClass:
LP
Totalvariables:
4
Nonlinearvariables:
0
Integervariables:
0
Totalconstraints:
4
Nonlinearconstraints:
0
Totalnonzeros:
15
Nonlinearnonzeros:
0
VariableValueReducedCost
X10.0000005.000000
X20.00000013.00000
X34.0000000.000000
X42.0000000.000000
RowSlackorSurplusDualPrice
1-0.1000000E+31-1.000000
20.0000003.000000
314.000000.000000
40.0000002.000000
min=2*x1-2*x2+3*x3;
-x1+x2+x3=4;
-2*x1+x2-x3<=6;
end
freex4;
Globaloptimalsolutionfound.
Objectivevalue:
-8.000000
Infeasibilities:
0.000000
Totalsolveriterations:
3
ModelClass:
LP
Totalvariables:
3
Nonlinearvariables:
0
Integervariables:
0
Totalconstraints:
3
Nonlinearconstraints:
0
Totalnonzeros:
9
Nonlinearnonzeros:
0
VariableValueReducedCost
X10.0000000.000000
X24.0000000.000000
X30.0000005.000000
1.3
max=3*x1+x2+2*x3;
12*x1+3*x2+6*x3+3*x4=9;
8*x1+x2-4*x3+2*x5=10;
3*x1-x6=0;
Globaloptimalsolutionfound.
Objectivevalue:
3.000000
Infeasibilities:
0.000000
Totalsolveriterations:
1
ModelClass:
LP
Totalvariables:
6
Nonlinearvariables:
0
Integervariables:
0
Totalconstraints:
4
Nonlinearconstraints:
0
Totalnonzeros:
13
Nonlinearnonzeros:
0
VariableValueReducedCost
X10.0000001.000000
X23.0000000.000000
X30.0000000.000000
X40.0000001.000000
X53.5000000.000000
X60.0000000.000000
RowSlackorSurplusDualPrice
13.0000001.000000
20.0000000.3333333
30.0000000.000000
40.0000000.000000
min=5*x1-2*x2+3*x3+2*x4;
x1+2*x2+3*x3+4*x4=7;
2*x1+2*x2+x3+2*x4=3;
Globaloptimalsolutionfound.
Objectivevalue:
5.000000
Infeasibilities:
0.000000
Totalsolveriterations:
2
ModelClass:
LP
Totalvariables:
4
Nonlinearvariables:
0
Integervariables:
0
Totalconstraints:
3
Nonlinearconstraints:
0
Totalnonzeros:
12
Nonlinearnonzeros:
0
VariableValueReducedCost
X10.0000009.000000
X20.50000000.000000
X32.0000000.000000
X40.0000000.000000
RowSlackorSurplusDualPrice
15.000000-1.000000
20.000000-2.000000
30.0000003.000000
1.4
max=10*x1+5*x2;
3*x1+4*x2<=9;
5*x1+2*x2<=8;
Globaloptimalsolutionfound.
Objectivevalue:
17.50000
Infeasibilities:
0.000000
Totalsolveriterations:
2
ModelClass:
LP
Totalvariables:
2
Nonlinearvariables:
0
Integervariables:
0
Totalconstraints:
3
Nonlinearconstraints:
0
Totalnonzeros:
6
Nonlinearnonzeros:
0
VariableValueReducedCost
X11.0000000.000000
X21.5000000.000000
RowSlackorSurplusDualPrice
117.500001.000000
20.0000000.3571429
30.0000001.785714
max=2*x1+x2;
3*x1+5*x2<=15;
6*x1+2*x2<=24;
Globaloptimalsolutionfound.
Objectivevalue:
8.250000
Infeasibilities:
0.000000
Totalsolveriterations:
2
ModelClass:
LP
Totalvariables:
2
Nonlinearvariables:
0
Integervariables:
0
Totalconstraints:
3
Nonlinearconstraints:
0
Totalnonzeros:
6
Nonlinearnonzeros:
0
VariableValueReducedCost
X13.7500000.000000
X20.75000000.000000
RowSlackorSurplusDualPrice
18.2500001.000000
20.0000000.8333333E-01
30.0000000.2916667
1.6
max=c1*x1+c2*x2;
a11*x1+a12*x2<=b1;
a21*x1+a22*x2<=b2;
c1>=1;c1<=3;
c2>=4;c2<=6;
a11>=-1;a11<=3;
a12>=2;a12<=5;
a21>=2;a21<=5;
a22>=4;a22<=6;
b2>=10;b2<=14;
Localoptimalsolutionfound.
Objectivevalue:
21.00000
Infeasibilities:
0.000000
Totalsolveriterations:
13
ModelClass:
NLP
Totalvariables:
10
Nonlinearvariables:
8
Integervariables:
0
Totalconstraints:
17
Nonlinearconstraints:
3
Totalnonzeros:
28
Nonlinearnonzeros:
12
VariableValueReducedCost
C12.0212920.000000
X10.0000000.9787081
C26.0000000.000000
X23.5000000.000000
A111.2345680.000000
A122.2401540.000000
B18.3515460.000000
A212.0000000.000000
A224.0000000.000000
B214.000000.000000
RowSlackorSurplusDualPrice
121.000001.000000
20.51100580.000000
30.0000001.500000
41.0212920.000000
50.97870810.000000
62.0000000.000000
70.0000003.500000
82.2345680.000000
91.7654320.000000
100.24015430.000000
112.7598460.000000
120.0000000.000000
133.0000000.000000
140.000000-5.250000
152.0000000.000000
164.0000000.000000
170.0000001.500000
1.7
max=2*x1-x2+2*x3;
x1+x2+x3>=6;
-2*x1+x3>=2;
2*x2-x3>=0;
Modelisunbounded
ModelClass:
LP
Totalvariables:
3
Nonlinearvariables:
0
Integervariables:
0
Totalconstraints:
4
Nonlinearconstraints:
0
Totalnonzeros:
10
Nonlinearnonzeros:
0
VariableValueReducedCost
X10.75000000.000000
X21.7500000.000000
X33.5000000.000000
RowSlackorSurplusDualPrice
1-0.1000000E+311.000000
20.0000001.250000
30.000000-0.3750000
40.000000-1.125000
min=2*x1+3*x2+x3;
x1+4*x2+2*x3>=8;
3*x1+2*x2>=6;
Globaloptimalsolutionfound.
Objectivevalue:
7.000000
Infeasibilities:
0.000000
Totalsolveriterations:
3
ModelClass:
LP
Totalvariables:
3
Nonlinearvariables:
0
Integervariables:
0
Totalconstraints:
3
Nonlinearconstraints:
0
Totalnonzeros:
8
Nonlinearnonzeros:
0
VariableValueReducedCost
X10.80000000.000000
X21.8000000.000000
X30.0000000.000000
min=4*x1+x2;
3*x1+x2=3;
4*x1+3*x2-x3=6;
x1+2*x2+x4=4;
Globaloptimalsolutionfound.
Objectivevalue:
3.400000
Infeasibilities:
0.000000
Totalsolveriterations:
0
ModelClass:
LP
Totalvariables:
4
Nonlinearvariables:
0
Integervariables:
0
Totalconstraints:
4
Nonlinearconstraints:
0
Totalnonzeros:
10
Nonlinearnonzeros:
0
VariableValueReducedCost
X10.40000000.000000
X21.8000000.000000
X31.0000000.000000
X40.0000000.2000000
RowSlackorSurplusDualPrice
13.400000-1.000000
20.000000-1.400000
30.0000000.000000
40.0000000.2000000
max=10*x1+15*x2+12*x3;
5*x1+3*x2+x3<=9;
-5*x1+6*x2+15*x3<=15;
2*x1+x2+x3>=5;
Nofeasiblesolutionfound.
Infeasibilities:
0.9302326
Totalsolveriterations:
3
ModelClass:
LP
Totalvariables:
3
Nonlinearvariables:
0
Integervariables:
0
Totalconstraints:
4
Nonlinearconstraints:
0
Totalnonzeros:
12
Nonlinearnonzeros:
0
VariableValueReducedCost
X11.9534880.000000
X2-0.93023260.000000
X32.0232560.000000
RowSlackorSurplusDualPrice
10.93023261.000000
20.0000005.372093
30.0000000.8604651
40.000000-6.279070
例9
max=0.9*x11+1.4*x21+1.9*x31+0.95*x12+0.95*x22+1.45*x32-0.05*x13+1.45*x23+0.95*x33;
x11+x12+x13<=2000;
x21+x22+x23<=2500;
x31+x32+x33<=1200;
x11>=0.6*（x11+x21+x31）;
x31<=0.2*（x11+x21+x31）;
x12>=0.3*（x12+x22+x32）;
x32<=0.5*（x12+x22+x32）;
x33<=0.6*（x13+x23+x33）;
Globaloptimalsolutionfound.
Objectivevalue:
7365.000
Infeasibilities:
0.000000
Totalsolveriterations:
6
ModelClass:
LP
Totalvariables:
9
Nonlinearvariables:
0
Integervariables:
0
Totalconstraints:
9
Nonlinearconstraints:
0
Totalnonzeros:
33
Nonlinearnonzeros:
0
VariableValueReducedCost
X111200.0000.000000
X21400.00000.000000
X31400.00000.000000
X12800.00000.000000
X220.0000000.3750000
X32800.00000.000000
X130.0000001.125000
X232100.0000.000000
X330.0000000.3750000
RowSlackorSurplusDualPrice
17365.0001.000000
20.0000001.075000
30.0000001.450000
40.0000001.325000
50.000000-0.1250000
60.0000000.6250000
7320.00000.000000
80.0000000.2500000
91260.0000.000000
1.15先列出线性规划问题如下：
Maxz=1000*（x11+x12+x13）+700*（x21+x22+x23）+600*（x31+x32+x33）;
8*x11+6*x21+5*x31<=2000;
8*x12+6*x22+5*x32<=3000;
8*x13+6*x23+5*x33<=1500;
10*x11+5*x21+7*x31<=4000;
10*x12+5*x22+7*x32<=5400;
10*x13+5*x23+7*x33<=1500;
（8*x12+6*x22+5*x3
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