Investigacion De Opraciones
Páginas: 10 (2275 palabras)
Publicado: 10 de julio de 2011
ZMIN : 600 X1 + 400 X2 |
2 X1 + 1 X2 ≤ 8
6 X1 + 2 X2 ≤ 12
1 X1 + 3 X2 ≤ 9 |
X1, X2 ≥ 0 |
TRABAJO DE CAMPO I – INVESTIGACIÓN DE OPERACIONES I
EJERCICIO 1
ZMAX: -600 X1 -400 X2 + 0 H1 + 0 H2 + 0 H3 |
2 X1 + 1 X2 + 1 H1 = 8
6 X1 + 2 X2 + 1 H2= 12
1 X1 + 3 X2 + 1 H3 = 9 |
X1, X2, H1,H2,H3 ≥ 0 |
La solución optima es Z =0
X1 = 0
X2= 0
ZMAX+600+400-H1-H2-H3 =0
| | || | | | | |
| BASICA | Z | X1 | X2 | H1 | H2 | H3 | SOLUCION |
| | | | | | | | |
| 0 | 1 | 600 | 400 | 0 | 0 | 0 | 0 |
| H1 | 0 | 2 | 1 | 1 | 0 | 0 | 8 |
| H2 | 0 | 6 | 2 | 0 | 1 | 0 | 12 |
| H3 | 0 | 1 | 3 | 0 | 0 | 1 | 9 |
MÉTODO SIMPLEX
MÉTODO DUAL SIMPLEX
| A | B | Necesidad |
PROTEÍNAS | 2 | 1 | 8 |
HIDRATOS | 6 | 1 | 12 |
GRASAS | 1 | 3 | 9|
Min Z=600x1+400x2 | Multiplicado por -1 >>> | | Max *Z=-600x1-400x2-MA1-MA2-MA3 |
Sujeto a: | | | | |
| Sujeto a: | | |
2x1+x2<=8 | | Multiplicando por -1 y
convirtiendo las
inecuaciones en ecuaciones
agregando variables de holgura. | -2x1-x2+H1=8 | |
6x1+x2<=12 | | | -2x1-x2+H2=12 | |
x1+3x2<=9 | | | -x1-3x2+H3=9 | |
x>=0 ; y>=0| | | x>=0 ; y>=0 | | |
ITERACIÓN | VB | nº EC | x1 | x2 | H1 | H2 | H3 | SOLUCION |
0 | Z | 0 | 600 | 400 | 0 | 0 | 0 | 0 |
| H1 | 1 | -2 | -1 | 1 | 0 | 0 | -8 |
| H2 | 2 | -6 | -1 | 0 | 1 | 0 | -12 |
| H3 | 3 | -1 | -3 | 0 | 0 | 1 | -9 |
1 | Z | 0 | 0 | 300 | 0 | 0 | 0 | -1200 |
| H1 | 1 | 0 | 2/3 | 1 | - 1/3 | 0 | -4 |
| X1 | 2 | 1 | 1/6 | 0 | - 1/6 | 0 | 2 || H3 | 3 | 0 | -17/6 | 0 | - 1/6 | 1 | -7 |
2 | Z | 0 | 0 | 0 | 0 | -5100 | -1800/17 | -33000/17 |
| H1 | 1 | 0 | 0 | 1 | 35/3 | 4/17 | -96/17 |
| X1 | 2 | 1 | 0 | 0 | -3 | 1/17 | 27/17 |
| X2 | 3 | 0 | 1 | 0 | 17 | -6/17 | 42/17 |
La solución óptima para el modelo Z=-33000/17 ES IGUAL A 1941.17647
Comprando semanalmente: |
X1 | 27/17 ES IGUAL A 1.6 | Kilogramos |
X2 |42/17 ES IGUAL A 2.5 | Kilogramos |
EJERCICIO 2 ZMAX =1000X1+800X2+400X3
550X1+1000X2+50X3<=700
650X1+8500X2+75X3<=850
300X1+4000X2+40X3<=750
X1>=0; X2>=0; X3>=0
ZMAX =1000X1+800X2+400X3+0H1+0H2+0H3 ZMAX -1000X1-800X2-400X3-0H1-0H2-0H3=0
550X1+1000X2+50X3+H1+0H2+0H3<=700
650X1+8500X2+75X3+0H1+H2+0H3<=850
300X1+4000X2+40X3+0H1+0H2+H3<=750
X1,X2, X3, H1, H2, H3 >= 0
METODO SIMPLEX:
cj | | | 1000 | 800 | 400 | 0 | 0 | 0 |
| | SOLUCION | X1 | X2 | X3 | H1 | H2 | H3 |
0 | H1 | 700 | 550 | 10000 | 50 | 1 | 0 | 0 |
00 | H2H3 | 850750 | 650300 | 85004000 | 7540 | 00 | 10 | 01 |
ZjZj-Cj | | 0 | 0-1000 | 0-800 | 0-400 | 00 | 00 | 00 |
1000 | X1 | 14/11 | 1 | 200/11 | 1/11 | 1/550 | 0 | 0 |
0 | H2 | 250/11 | 0 |-36500/11 | 175/11 | -13/11 | 1 | 0 |
0 | H3 | 4050/11 | 0 | -16000/11 | 140/11 | -6/11 | 0 | 1 |
ZjZj-Cj | | 14000/11 | 10000 | 200000/11191200/11 | 1000/11-3400/11 | 20/1120/11 | 00 | 00 |
400 | X3 | 10/7 | 0 | -1460/7 | 1 | -13/175 | 11/175 | 0 |
1000 | X1 | 8/7 | 1 | 260/7 | 0 | 3/350 | -1/175 | 0 |
0 | H3 | 350 | 0 | 1200 | 0 | 2/5 | -4/5 | 1 |
ZjZj-Cj | | 12000/7 | 10000 |-329600/7-329600/7 | 4000 | -148/7-148/7 | 136/7136/7 | 00 |
04000 | H1X3H3 | 400/334/3-84950/3 | 350/326/3-75250/3 | 13000/3340/3-2791400/3 | 010 | 100 | -2/31/752138/15 | 001 |
Zj | | 13600/3 | 10400/3 | 136000/3 | 400 | 0 | 400/75 | 0 |
Zj=13600/3 ES IGUAL A 4533.3333
X3=34/3 ES IGUAL A 11.33
Es la solución óptima
POR LINDO:
Max 1000x1+800x2+400x3
Subject to
550x1+1000x2+50x3<=700650x1+8500x2+75x3<=850
300x1+4000x2+40x3<=750
Global optimal solution found.
Objective value: 4533.333
Total solver iterations: 3
Variable Value Reduced Cost
X1 0.000000 2466.667
X2 0.000000...
2 X1 + 1 X2 ≤ 8
6 X1 + 2 X2 ≤ 12
1 X1 + 3 X2 ≤ 9 |
X1, X2 ≥ 0 |
TRABAJO DE CAMPO I – INVESTIGACIÓN DE OPERACIONES I
EJERCICIO 1
ZMAX: -600 X1 -400 X2 + 0 H1 + 0 H2 + 0 H3 |
2 X1 + 1 X2 + 1 H1 = 8
6 X1 + 2 X2 + 1 H2= 12
1 X1 + 3 X2 + 1 H3 = 9 |
X1, X2, H1,H2,H3 ≥ 0 |
La solución optima es Z =0
X1 = 0
X2= 0
ZMAX+600+400-H1-H2-H3 =0
| | || | | | | |
| BASICA | Z | X1 | X2 | H1 | H2 | H3 | SOLUCION |
| | | | | | | | |
| 0 | 1 | 600 | 400 | 0 | 0 | 0 | 0 |
| H1 | 0 | 2 | 1 | 1 | 0 | 0 | 8 |
| H2 | 0 | 6 | 2 | 0 | 1 | 0 | 12 |
| H3 | 0 | 1 | 3 | 0 | 0 | 1 | 9 |
MÉTODO SIMPLEX
MÉTODO DUAL SIMPLEX
| A | B | Necesidad |
PROTEÍNAS | 2 | 1 | 8 |
HIDRATOS | 6 | 1 | 12 |
GRASAS | 1 | 3 | 9|
Min Z=600x1+400x2 | Multiplicado por -1 >>> | | Max *Z=-600x1-400x2-MA1-MA2-MA3 |
Sujeto a: | | | | |
| Sujeto a: | | |
2x1+x2<=8 | | Multiplicando por -1 y
convirtiendo las
inecuaciones en ecuaciones
agregando variables de holgura. | -2x1-x2+H1=8 | |
6x1+x2<=12 | | | -2x1-x2+H2=12 | |
x1+3x2<=9 | | | -x1-3x2+H3=9 | |
x>=0 ; y>=0| | | x>=0 ; y>=0 | | |
ITERACIÓN | VB | nº EC | x1 | x2 | H1 | H2 | H3 | SOLUCION |
0 | Z | 0 | 600 | 400 | 0 | 0 | 0 | 0 |
| H1 | 1 | -2 | -1 | 1 | 0 | 0 | -8 |
| H2 | 2 | -6 | -1 | 0 | 1 | 0 | -12 |
| H3 | 3 | -1 | -3 | 0 | 0 | 1 | -9 |
1 | Z | 0 | 0 | 300 | 0 | 0 | 0 | -1200 |
| H1 | 1 | 0 | 2/3 | 1 | - 1/3 | 0 | -4 |
| X1 | 2 | 1 | 1/6 | 0 | - 1/6 | 0 | 2 || H3 | 3 | 0 | -17/6 | 0 | - 1/6 | 1 | -7 |
2 | Z | 0 | 0 | 0 | 0 | -5100 | -1800/17 | -33000/17 |
| H1 | 1 | 0 | 0 | 1 | 35/3 | 4/17 | -96/17 |
| X1 | 2 | 1 | 0 | 0 | -3 | 1/17 | 27/17 |
| X2 | 3 | 0 | 1 | 0 | 17 | -6/17 | 42/17 |
La solución óptima para el modelo Z=-33000/17 ES IGUAL A 1941.17647
Comprando semanalmente: |
X1 | 27/17 ES IGUAL A 1.6 | Kilogramos |
X2 |42/17 ES IGUAL A 2.5 | Kilogramos |
EJERCICIO 2 ZMAX =1000X1+800X2+400X3
550X1+1000X2+50X3<=700
650X1+8500X2+75X3<=850
300X1+4000X2+40X3<=750
X1>=0; X2>=0; X3>=0
ZMAX =1000X1+800X2+400X3+0H1+0H2+0H3 ZMAX -1000X1-800X2-400X3-0H1-0H2-0H3=0
550X1+1000X2+50X3+H1+0H2+0H3<=700
650X1+8500X2+75X3+0H1+H2+0H3<=850
300X1+4000X2+40X3+0H1+0H2+H3<=750
X1,X2, X3, H1, H2, H3 >= 0
METODO SIMPLEX:
cj | | | 1000 | 800 | 400 | 0 | 0 | 0 |
| | SOLUCION | X1 | X2 | X3 | H1 | H2 | H3 |
0 | H1 | 700 | 550 | 10000 | 50 | 1 | 0 | 0 |
00 | H2H3 | 850750 | 650300 | 85004000 | 7540 | 00 | 10 | 01 |
ZjZj-Cj | | 0 | 0-1000 | 0-800 | 0-400 | 00 | 00 | 00 |
1000 | X1 | 14/11 | 1 | 200/11 | 1/11 | 1/550 | 0 | 0 |
0 | H2 | 250/11 | 0 |-36500/11 | 175/11 | -13/11 | 1 | 0 |
0 | H3 | 4050/11 | 0 | -16000/11 | 140/11 | -6/11 | 0 | 1 |
ZjZj-Cj | | 14000/11 | 10000 | 200000/11191200/11 | 1000/11-3400/11 | 20/1120/11 | 00 | 00 |
400 | X3 | 10/7 | 0 | -1460/7 | 1 | -13/175 | 11/175 | 0 |
1000 | X1 | 8/7 | 1 | 260/7 | 0 | 3/350 | -1/175 | 0 |
0 | H3 | 350 | 0 | 1200 | 0 | 2/5 | -4/5 | 1 |
ZjZj-Cj | | 12000/7 | 10000 |-329600/7-329600/7 | 4000 | -148/7-148/7 | 136/7136/7 | 00 |
04000 | H1X3H3 | 400/334/3-84950/3 | 350/326/3-75250/3 | 13000/3340/3-2791400/3 | 010 | 100 | -2/31/752138/15 | 001 |
Zj | | 13600/3 | 10400/3 | 136000/3 | 400 | 0 | 400/75 | 0 |
Zj=13600/3 ES IGUAL A 4533.3333
X3=34/3 ES IGUAL A 11.33
Es la solución óptima
POR LINDO:
Max 1000x1+800x2+400x3
Subject to
550x1+1000x2+50x3<=700650x1+8500x2+75x3<=850
300x1+4000x2+40x3<=750
Global optimal solution found.
Objective value: 4533.333
Total solver iterations: 3
Variable Value Reduced Cost
X1 0.000000 2466.667
X2 0.000000...
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