Trabajo simplex

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  • Publicado : 16 de junio de 2010
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Minimizar Z = 6X1 + 4X2 + 2X3
C.S.R.
8X1 + 4X2 + 8X3 >= 8
8X1 + 6X2 = 14
4X1 - 4X2 <= 4
Xj > 0 ; j = 1, 2, 3

Cj | | | 6 | 4 | 2 | 0 | M | M | 0 |
| VB | b | X1 | X2 | X3 | X4 | X5 | X6 | X7 |
M | X5 | 8 | 8 | 4 | 8 | -1 | 1 | 0 | 0 |
M | X6 | 14 | 8 | 6 | 0 | 0 | 0 | 1 | 0 |
0 | X7 | 4 | 4 | -4 | 0 | 0 | 0 | 0 | 1 |
Zj-Cj | | 22M | 16M-6 | 10M-4 | 8M-2 | -M| 0 | 0 | 0 |

Cj | | | 6 | 4 | 2 | 0 | M | M | 0 |
| VB | b | X1 | X2 | X3 | X4 | X5 | X6 | X7 |
6 | X1 | 1 | 1 | 0.5 | 1 | -0.125 | 0.125 | 0 | 0 |
M | X6 | 6 | 0 | 2 | -8 | 1 | -1 | 1 | 0 |
0 | X7 | 0 | 0 | -6 | -4 | 0.5 | -0.5 | 0 | 1 |
Zj-Cj | | 6M+6 | 0 | 2M-1 | -8M+4 | M-0.75 | -2M+0.75 | M | 0 |

Cj | | | 6 | 4 | 2 | 0 | M | M | 0 |
| VB | b | X1 | X2 | X3 | X4 |X5 | X6 | X7 |
4 | X2 | 2 | 2 | 1 | 2 | -0.25 | 0.25 | 0 | 0 |
M | X6 | 2 | -4 | 0 | -12 | 1.5 | -1.5 | 1 | 0 |
0 | X7 | 12 | 12 | 0 | 8 | -1 | 1 | 0 | 1 |
Zj-Cj | | | -4M+14 | 0 | -12M+6 | 1.5M-1 | -2.5M+1 | 0 | 0 |

Cj | | | 6 | 4 | 2 | 0 | M | M | 0 |
| VB | b | X1 | X2 | X3 | X4 | X5 | X6 | X7 |
4 | X2 | 2.33 | 1.33 | 1 | 0 | 0 | 0 | 0.16 | 0 |
0 | X4 | 1.33 | -2.66 | 0 |-8 | 1 | -1 | 0.66 | 0 |
0 | X7 | 13.33 | 9.34 | 0 | 0 | 0 | 0 | 0.66 | 1 |
Zj-Cj | | | -0.66 | 0 | -2 | 0 | -M | -M+0.64 | 0 |
X1=0 X4=1.33
X2=2.33 X5=0
X3=0 X6=0
X7=13.33

Respuesta:

Maximizar Z = 5X1 + 2X2
3X1 + 6X2 >=18
5X1 + 4X2 >= 20
8X1 + 2X2 >= 16
7X1 + 6X2 <= 42
Xj > 0 ; j = 1, 2

Cj | | | 5 | 2 | 0 | -M | 0 | -M | 0 | -M | 0 |
| VB |b | X1 | X2 | X3 | X4 | X5 | X6 | X7 | X8 | X9 |
-M | X4 | 18 | 3 | 6 | -1 | 1 | 0 | 0 | 0 | 0 | 0 |
-M | X6 | 20 | 5 | 4 | 0 | 0 | -1 | 1 | 0 | 0 | 0 |
-M | X8 | 16 | 8 | 2 | 0 | 0 | 0 | 0 | -1 | 1 | 0 |
0 | X9 | 42 | 7 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
Zj-Cj | | | -16M-5 | -12M-2 | M | 0 | M | 0 | M | 0 | 0 |
Cj | | | 5 | 2 | 0 | -M | 0 | -M | 0 | -M | 0 |
| VB | b | X1 | X2| X3 | X4 | X5 | X6 | X7 | X8 | X9 |
-M | X4 | 12 | 0 | 5,25 | -1 | 1 | 0 | 0 | 0.375 | -0.375 | 0 |
-M | X6 | 10 | 0 | 2.75 | 0 | 0 | -1 | 1 | 0.625 | -0.625 | 0 |
5 | X1 | 2 | 1 | .25 | 0 | 0 | 0 | 0 | -.125 | .125 | 0 |
0 | X9 | 28 | 0 | 4.25 | 0 | 0 | 0 | 0 | 0.875 | -0.875 | 1 |
Zj-Cj | | | 0 | -8M-0.75 | M | 0 | M | 0 | -M-0.625 | 2M+0.625 | 0 |

Cj | | | 5 | 2 | 0 | -M | 0| -M | 0 | -M | 0 |
| VB | b | X1 | X2 | X3 | X4 | X5 | X6 | X7 | X8 | X9 |
2 | X2 | 2.285 | 0 | 1 | -0.1905 | 0.195 | 0 | 0 | 0.0714 | -0.0714 | 0 |
-M | X6 | 3.714 | 0 | 0 | 0.5238 | -0.5238 | -1 | 1 | 0.4286 | -0.4286 | 0 |
5 | X1 | 1.428 | 1 | 0 | 0.0476 | -0.0476 | 0 | 0 | -0.1429 | 0.1429 | 0 |
0 | X9 | 18.28 | 0 | 0 | 0.8095 | -0.8095 | 0 | 0 | 0.5714 | -0.5714 | 1 |
Zj-Cj | || 0 | 0 | -0.666 | 1.52M+0.15 | M | 0 | -0.4286M-0.57 | 1.428M+0.57 | 0 |

Cj | | | 5 | 2 | 0 | -M | 0 | -M | 0 | -M | 0 |
| VB | b | X1 | X2 | X3 | X4 | X5 | X6 | X7 | X8 | X9 |
2 | X2 | 1.66 | 0 | 1 | -0.277 | 0.277 | 0.166 | -0.166 | 0 | 0 | 0 |
0 | X7 | 8.66 | 0 | 0 | 1.22 | -1.22 | -2.33 | 2.33 | 1 | -1 | 0 |
5 | X1 | 2.66 | 1 | 0 | 0.22 | -0.22 | -0.333 | 0.333 | 0 | 0 | 0 |0 | X9 | 13.33 | 0 | 0 | 0.11 | -0.11 | 1.33 | -1.33 | 0 | 0 | 1 |
Zj-Cj | | | | | | | | | | | |

Cj | | | 5 | 2 | 0 | -M | 0 | -M | 0 | -M | 0 |
| VB | b | X1 | X2 | X3 | X4 | X5 | X6 | X7 | X8 | X9 |
0 | X5 | 10 | 0 | 6 | -1.66 | 1.66 | 1 | -1 | 0 | 0 | 0 |
0 | X7 | 32 | 0 | 14 | -2.66 | 2.66 | 0 | 0 | 1 | -1 | 0 |
5 | X1 | 6 | 1 | 2 | -0.33 | 0.33 | 0 | 0 | 0 | 0 |0 |
0 | X9 | 0 | 0 | 8 | 2.33 | -2.33 | 0 | 0 | 0 | 0 | 1 |
Zj-Cj | | | | | | | | | | | |

Cj | | | 5 | 2 | 0 | -M | 0 | -M | 0 | -M | 0 |
| VB | b | X1 | X2 | X3 | X4 | X5 | X6 | X7 | X8 | X9 |
0 | X5 | 10 | 0 | 0.285 | 0 | 0 | 1 | -1 | 0 | 0 | 0.714 |
0 | X7 | 32 | 0 | 4.857 | 0 | 0 | 0 | 0 | 1 | -1 | 1.142 |
5 | X1 | 6 | 1 | 0.857 | 0 | 0 | 0 | 0 | 0 | 0 | 0.142 |...
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