# Investigación de operaciones

Páginas: 11 (2700 palabras) Publicado: 6 de septiembre de 2010
INSTITUTO TECNOLÓGICO DE CELAYA.

DEPARTAMENTO DE INGENIERÍA INDUSTRIAL.

MATERIA: INVESTIGACIÓN DE OPERACIONES I.

EJERCICIOS MÉTODO SIMPLEX

CELAYA GTO. 20-04-10
MIN Z = 50X1 + 20X2 |
s.a | | | | |
2X1 | - | X2 | ≥ | 0 |
X1 | + | 4X2 | ≥ | 80|
0.9X1 | + | 0.8X2 | ≥ | 40 |
| | X1, X2 | ≥ | 0 |
1.-

| | Cj | 50 | 20 | 0 | 0 | 0 | M | M | |
CB | XB | Sol | X1 | X2 | S1 | S2 | S3 | A1 | A3 | Ri |
0 | S1 | 0 | -2 | 1 | 1 | 0 | 0 | 0 | 0 | sale
0 |
M | A2 | 80 | 1 | 4 | 0 | -1 | 0 | 1 | 0 | 20 |
M | A3 | 40 | 0.9 | 0.8 | 0 | 0 | -1 | 0 | 1 | 50 |
| Zj | | -0.1M | 4.8M | -M | -M | -M | M | M | |
| | Zj-Cj| -.1M-2 | 4.8M-3 | -M | -M | -M | 0 | 0 | |
entra

| | Cj | 50 | 20 | 0 | 0 | 0 | M | M | |
CB | XB | Sol | X1 | X2 | S1 | S2 | S3 | A1 | A3 | Ri |
20 | X2 | 0 | -2 | 1 | 1 | 0 | 0 | 0 | 0 | sale
- |
M | A2 | 80 | 9 | 0 | -4 | -1 | 0 | 1 | 0 | 8.8 |
M | A3 | 40 | 2.5 | 0 | -0.8 |0 | -1 | 0 | 1 | 16 |
| Zj | | 11M-40 | 20 | -4.8M+20 | -M | M | -M | -M | |
| | Zj-Cj | 11M-90 | 0 | -4.8M+20 | -M | M | -2M | -2M | |
entra

| | Cj | 50 | 20 | 0 | 0 | 0 | M | M | |
CB | XB | Sol | X1 | X2 | S1 | S2 | S3 | A1 | A3 | Ri |
20 | X2 | 17.7 | 0 | 1 | 0.1 | -0.22 | 0 | 0.22 | 0 | 160 |
50 | X1 | 8.8 | 1| 0 | -0.4 | -0.1 | 0 | 0.11 | 0 | sale
- |
M | A3 | 17.7 | 0 | 0 | 0.3 | 0.27 | -1 | -0.27 | 1 | 57.14 |
| Zj | | 50 | 20 | 18+0.3M | -9.4+0.27M | -M | -.27M | -M | |
| | Zj-Cj | 50 | 20 | 0.3M+18 | -9.4+0.27M | -M | -2.27M | -2M | |
entra

| | Cj | 50 | 20 | 0 | 0 | 0 | M | M | |
CB | XB |Sol | X1 | X2 | S1 | S2 | S3 | A1 | A3 | Ri |
20 | X2 | 11.42 | 0 | 1 | 0 | -0.32 | 0.35 | 0.35 | -0.35 | - |
50 | X1 | 34.28 | 1 | 0 | 0 | 0.28 | -1.42 | 1.42 | 1.42 | sale
120 |
0 | S1 | 57.14 | 0 | 0 | 1 | 0.89 | -3.21 | 3.21 | 3.21 | 64 |
| Zj | 1942 | 50 | 20 | 0 | 7.6 | -64 | 78 | 64 | |
| | Zj-Cj | 0 | 0 | 0 | 7.6 | -64 | 78-M | 64-M | |entra

| | Cj | 50 | 20 | 0 | 0 | 0 | M | M | |
CB | XB | Sol | X1 | X2 | S1 | S2 | S3 | A1 | A3 | Ri |
20 | X2 | 32 | 0 | 1 | 0.36 | 0 | -0.80 | 0 | 0.8 | |
50 | X1 | 16 | 1 | 0 | -0.32 | 0 | -0.40 | 0 | 0.4 | |
0 | S2 | 64 | 0 | 0 | 1.12 | 1 | -3.60 | -1 | 3.6 | |
| Zj | 1440| 50 | 20 | -8.8 | 0 | -28 | 0 | 0 | |
| | Zj-Cj | 0 | 0 | -8.8 | 0 | -28 | -M | 36-M | |

Solución: optima, básica, factible, única, no degenerada.

Min Z = 80X1 + 60X2 |
s.a | | | | |
X1 | + | X2 | = | 200 |
X1 | | | ≤ | 50 |
| | X2 | ≥ | 80 |
| | X1, X2 | ≥ | 0 |
2.-

| | Cj | 80 | 60 | 0 | 0 | -M | -M | |
CB | XB | Sol | X1 | X2 |S2 | S3 | A1 | A3 | Ri |
-M | A1 | 200 | 1 | 1 | 0 | 0 | 1 | 0 | 200 |
0 | S2 | 50 | 1 | 0 | 1 | 0 | 0 | 0 | sale
- |
-M | A3 | 880 | 0 | 1 | 0 | -1 | 1 | 1 | 80 |
| Zj | | -M | -2M | 0 | -M | -M | -M | |
| | Zj-Cj | -M-2 | -2M-60 | 0 | -M | 0 | 0 | |
entra

| | Cj | 80 | 60 | 0 | 0 | -M | -M | |CB | XB | Sol | X1 | X2 | S2 | S3 | A1 | A3 | Ri |
-M | A1 | 120 | 1 | 1 | 0 | 1 | 1 | -1 | sale
120 |
0 | S2 | 50 | 1 | 0 | 1 | 0 | 0 | 0 | 50 |
60 | X2 | 880 | 0 | 1 | 0 | -1 | 1 | 1 | - |
| Zj | | -M | 60 | 0 | -M-60 | -M | M+60 | |
| | Zj-Cj | -M-80 | 0 | 0 | -M-60 | 0 | 2M+60 | |
entra

| | Cj | 80 | 60...

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