建模上机习题全解.docx
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建模上机习题全解.docx
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建模上机习题全解
1.
model:
max=0.043*x1+0.027*x2+0.025*x3+0.022*x4+0.045*x5;
x1+x2+x3>4;
x1+x2+x3+x4+x5<10;
6*x1+6*x2-4*x3-4*x4+36*x5<0;
4*x1+10*x2-x3-2*x4-3*x5<0;
x1>0;
x2>0;
x3>0;
x4>0;
x5>0;
end
Globaloptimalsolutionfound.
Objectivevalue:
0.2983636
Totalsolveriterations:
5
VariableValueReducedCost
X12.1818180.000000
X20.0000000.3018182E-01
X37.3636360.000000
X40.0000000.6363636E-03
X50.45454550.000000
RowSlackorSurplusDualPrice
10.29836361.000000
25.5454550.000000
30.0000000.2983636E-01
40.0000000.6181818E-03
50.0000000.2363636E-02
62.1818180.000000
70.0000000.000000
87.3636360.000000
90.0000000.000000
100.45454550.000000
2.
model:
max=63*x12+76*x13+71*x23+50*x24+85*x25+63*x34+77*x45+39*x46+92*x47+74*x56+89*x67;
x12+x13+x23+x24+x25+x34+x45+x46+x47+x56+x67<2;
x12+x13<1;
x12+x23+x24+x25<1;
x13+x23+x34<1;
x24+x45+x46+x47<1;
x25+x45+x56<1;
x46+x56+x67<1;
x47+x67<1;
end
@bin(x12);@bin(x13);@bin(x23);@bin(x24);@bin(x25);@bin(x34);
@bin(x45);@bin(x46);@bin(x47);@bin(x56);@bin(x67);
Globaloptimalsolutionfound.
Objectivevalue:
177.0000
Totalsolveriterations:
0
VariableValueReducedCost
X120.00000022.00000
X130.0000009.000000
X230.00000014.00000
X240.00000038.00000
X251.0000000.000000
X340.00000022.00000
X450.00000011.00000
X460.00000049.00000
X471.0000000.000000
X560.00000011.00000
X670.0000000.000000
RowSlackorSurplusDualPrice
1177.00001.000000
20.00000085.00000
31.0000000.000000
40.0000000.000000
51.0000000.000000
60.0000003.000000
70.0000000.000000
81.0000000.000000
90.0000004.000000
4
(1).
model:
min=s1+s2+s3+s4;
65*s1>6000+5*x1;
65*s2>7500+5*x2;
65*s3>5500+5*x3;
65*s4>9000+5*x4;
s1=120+x1;
s2=0.85*s1+x2;
s3=0.85*s2+x3;
s4=0.85*s3+x4;
x1>0;
x2>0;
x3>0;
x4>0;
s1>0;
s2>0;
s3>0;
s4>0;
end
Globaloptimalsolutionfound.
Objectivevalue:
478.5107
Totalsolveriterations:
1
VariableValueReducedCost
S1120.00000.000000
S2116.50000.000000
S399.025000.000000
S4142.98570.000000
X10.0000000.8732231
X214.500000.000000
X30.0000000.9291667
X458.814480.000000
RowSlackorSurplusDualPrice
1478.5107-1.000000
21800.0000.000000
30.000000-0.2982986E-01
4936.62500.000000
50.000000-0.1666667E-01
60.000000-0.8732231
70.0000000.1491493
80.000000-0.9291667
90.0000000.8333333E-01
100.0000000.000000
1114.500000.000000
120.0000000.000000
1358.814480.000000
14120.00000.000000
15116.50000.000000
1699.025000.000000
17142.98570.000000
4
(2).
model:
min=s1+s2+s3+s4;
65*s1>6000+5*x1;
65*s2>7500+5*x2;
65*s3>5500+5*x3;
65*s4>9000+5*x4;
s1=120+x1;
s2=0.85*s1+x2-y1;
s3=0.85*s2+x3-y2;
s4=0.85*s3+x4-y3;
x1>0;
x2>0;
x3>0;
x4>0;
s1>0;
s2>0;
s3>0;
s4>0;
y1>0;
y2>0;
y3>0;
end
Globaloptimalsolutionfound.
Objectivevalue:
465.1218
Totalsolveriterations:
0
VariableValueReducedCost
S1120.00000.000000
S2116.50000.000000
S384.615380.000000
S4144.00640.000000
X10.0000000.9291667
X214.500000.000000
X30.0000000.7147436E-01
X472.083330.000000
Y10.0000000.8333333E-01
Y214.409620.000000
Y30.0000000.8333333E-01
RowSlackorSurplusDualPrice
1465.1218-1.000000
21800.0000.000000
30.000000-0.1666667E-01
40.000000-0.1429487E-01
50.000000-0.1666667E-01
60.000000-0.9291667
70.0000000.8333333E-01
80.0000000.000000
90.0000000.8333333E-01
100.0000000.000000
1114.500000.000000
120.0000000.000000
1372.083330.000000
14120.00000.000000
15116.50000.000000
1684.615380.000000
17144.00640.000000
180.0000000.000000
1914.409620.000000
200.0000000.000000
6.
model:
max=(9-6*x1-16*x2-15*x4)*y1+(15-6*x1-16*x2-15*x4)*y2+(9-10)*z1+(15-10)*z2;
x4*(y1+y2)<50;
y1+z1<100;
y2+z2<200;
(3*x1+x2+x4-2.5)*y1-0.5*z1<0;
(3*x1+x2+x4-1.5)*y2+0.5*z2<0;
x1+x2+x4=1;
x1>0;
x2>0;
x4>0;
y1>0;
z1>0;
y2>0;
z2>0;
end
Localoptimalsolutionfound.
Objectivevalue:
450.0000
Totalsolveriterations:
8
VariableValueReducedCost
X10.000000200.0000
X20.49999990.000000
X40.50000010.000000
Y10.0000000.000000
Y2100.00000.000000
Z10.0000000.000000
Z2100.00000.000000
RowSlackorSurplusDualPrice
1450.00001.000000
2-0.1149344E-041.000000
3100.00000.000000
40.0000002.000000
50.0000002.000000
60.0000006.000000
70.000000-2200.000
80.0000000.000000
90.49999990.000000
100.50000010.000000
110.000000-4.000000
120.0000000.000000
13100.00000.000000
14100.00000.000000
7.Min=(x1+0.1*y1+x2+0.1*y2*2+x3+0.1*3*y3+x4+0.1*4*y4);
x1*r11+x2*r12+x3*r13+x4*r14>=15;
x1*r21+x2*r22+x3*r23+x4*r24>=28;
x1*r31+x2*r32+x3*r33+x4*r34>=21;
x1*r41+x2*r42+x3*r43+x4*r44>=30;
290*r11+315*r21+350*r31+455*r41>=1750*y1;
290*r12+315*r22+350*r32+455*r42>=1750*y2;
315*r23+350*r33+455*r43+290*r13>=1750*y3;
290*r14+315*r24+350*r34+455*r44>=1750*y4;
290*r11+315*r21+350*r31+455*r41<=1850*y1;
290*r12+315*r22+350*r32+455*r42<=1850*y2;
315*r23+350*r33+455*r43+290*r13<=1850*y3;
290*r14+315*r24+350*r34+455*r44<=1850*y4;
r11+r21+r31+r41>=y1;
r12+r22+r32+r42>=y2;
r13+r23+r33+r43>=y3;
r14+r24+r34+r44>=y4;
r11+r21+r31+r41<=5*y1;
r12+r22+r32+r42<=5*y2;
r13+r23+r33+r43<=5*y3;
r14+r24+r34+r44<=5*y4;
x1>=y1;
x2>=y2;
x3>=y3;
x4>=y4;
x1<=30*y1;
x2<=30*y2;
x3<=30*y3;
x4<=30*y4;
y2<=y1;
y3<=y2;
y4<=y3;
x2<=x1;
x3<=x2;
x4<=x3;
x1+x2+x3+x4>=19;
@gin(x1);@gin(x2);@gin(x3);@gin(x4);
@gin(r11);@gin(r21);@gin(r31);@gin(r41);
@gin(r12);@gin(r22);@gin(r32);@gin(r42);
@gin(r13);@gin(r23);@gin(r33);@gin(r43);
@gin(r14);@gin(r24);@gin(r34);@gin(r44);
end
~~2
Model:
Min=(x1+0.1+x2+0.1*2+x3+0.1*3+x4+0.1*4);
x1*r11+x2*r12+x3*r13+x4*r14>=15;
x1*r21+x2*r22+x3*r23+x4*r24>=28;
x1*r31+x2*r32+x3*r33+x4*r34>=21;
x1*r41+x2*r42+x3*r43+x4*r44>=30;
290*r11+315*r21+350*r31+455*r41>=1750;
290*r12+315*r22+350*r32+455*r42>=1750;
290*r13+315*r23+350*r33+455*r43>=1750;
290*r14+315*r24+350*r34+455*r44>=1750;
290*r11+315*r21+350*r31+455*r41<=1850;
290*r12+315*r22+350*r32+455*r42<=1850;
290*r13+315*r23+350*r33+455*r43<=1850;
290*r14+315*r24+350*r34+455*r44<=1850;
r11+r21+r31+r41>=1;
r12+r22+r32+r42>=1;
r13+r23+r33+r43>=1;
r14+r24+r34+r44>=1;
r11+r21+r31+r41<=5;
r12+r22+r32+r42<=5;
r13+r23+r33+r43<=5;
r14+r24+r34+r44<=5;
x1>=1;
x2>=1;
x3>=1;
x4>=1;
x1<=30;
x2<=30;
x3<=30;
x4<=30;
x2<=x1;
x3<=x2;
x4<=x3;
x1+x2+x3+x4>=19;
@gin(x1);@gin(x2);@gin(x3);@gin(x4);
@gin(r11);@gin(r21);@gin(r31);@gin(r41);
@gin(r12);@gin(r22);@gin(r32);@gin(r42);
@gin(r13);@gin(r23);@gin(r33);@gin(r43);
@gin(r14);@gin(r24);@gin(r34);@gin(r44);
end
Localoptimalsolutionfound.
Objectivevalue:
19.14000
Extendedsolversteps:
22
Totalsolveriterations:
789
VariableValueReducedCost
X119.000000.000000
Y11.4000000.000000
X20.0000000.000000
Y20.0000000.000000
X30.0000000.000000
Y30.0000000.000000
X40.0000000.000000
Y40.0000000.000000
R111.0000000.2000000E-01
R120.0000000.000000
R130.0000000.000000
R140.0000000.000000
R212.0000000.2000000E-01
R220.0000000.000000
R230.0000000.000000
R240.0000000.000000
R312.0000000.2000000E-01
R320.0000000.000000
R330.0000000.000000
R340.0000000.000000
R412.0000000.2000000E-01
R420.0000000.000000
R430.0000000.000000
R440.0000000.000000
RowSlackorSurplusDualPrice
119.14000-1.000000
24.0000000.000000
310.000000.000000
417.000000.000000
58.0000000.000000
680.000000.000000
70.0000000.000000
80.0000000.000000
90.0000000.000000
1060.000000.000000
110.0000000.000000
120.0000000.000000
130.0000000.000000
145.6000000.000000
150.0000000.000000
160.0000000.000000
170.0000000.000000
180.0000000.2000000E-01
190.0000000.000000
200.0000000.000000
210.0000000.000000
2217.600000.000000
230.000000-0.6896552E-02
240.000000-0.1034483E-01
250.000000-0.1379310E-01
2623.000000.000000
270.0000000.6896552E-02
280.0000000.1034483E-01
290.0000000.1379310E-01
301.4000000.000000
310.0000000.000000
320.0000000.000000
3319.000000.000000
340.0000000.000000
350.0000000.000000
360.000000-1.000000
8.
model:
max=200*(u1+u2)+140*(v1+v2);
400*xa1+200*xb1=u1+v1;
400*xa2+200*xb2=u2+v2;
xa1+ya1+za1=1900+200;
xb1+yb1+zb1=850+40+xa1+ya1;
xa2+ya2+za2=za1+130;
xb2+yb2+zb2=zb2+15+xa2+ya2;
400*xa1<60000;
400*xa2<60000;
200*xb1<35000;
200*xb2<35000;
za1>1200;
za1<2000;
za2>1200;
za2<2000;
zb1>800;
zb1<1500;
zb2>800;
zb2<1500;
u1<50000;
u2<50000;
end
Globaloptimalsolutionfound.
Objectivevalue:
0.3260000E+08
Totalsolveriterations:
10
VariableValueReducedCost
U150000.000.000000
U250000.000.000000
V145000.000.000000
V245000.000.000000
XA1150.00000.000000
XB1175.00000.000000
XA2150.00000.000000
XB2175.00000.000000
YA10.0000000.000000
ZA11950.0000.000000
YB10.0000000.000000
ZB1865.00000.000000
YA210.000000.000000
ZA21920.0000.000000
YB20.0000000.000000
ZB2800.00000.000000
RowSlackorSurplusDualPrice
10.3260000E+081.000000
20.000000-140.0000
30.000000-140.0000
40.0000000.000000
50.0000000.000000
60.0000000.000000
70.0000000.000000
80.000000140.0000
90.000000140.0000
100.000000140.0000
110.000000140.0000
12750.00000.000000
1350.000000.000000
14720.00000.000000
1580.000000.000000
1665.000000.000000
17635.00000.000000
180.0000000.000000
19700.00000.000000
200.00000060.00000
210.00000060.00000
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