Ejercicios Investigacion Operaciones

41.- max z=5x₁+12x₂+4x₃
s.a. x₁ +2x₂+x₃ ≤5
2x₁- x₂+3x₃ =2
x₁, x₂, x₃ ≥0

max z=5x₁+12x₂+4x₃-mw₂
x₁+ 2x₂+ x₃ +s₁ =5
2x₁- x₂+3x₃ +w₂=2
x₁, x₂, x₃ ≥0
BAS | Z | X₁ | X₂ | X₃ | S₁ | W₂ | SOL ||
Z | 1 | -5 | -12 | -4 | 0 | M | 0 | |
S₁ | 0 | 1 | 2 | 1 | 1 | 0 | 5 | |
W₂ | 0 | 2 | -1 | 3 | 0 | 1 | 2 | |

Ec. Z = | ( | 1 | -5 | -12 | -4 | 0 | M | 0 | ) |
Ec. W2(-M)= | ( | 0 | -2M | M | -3M | 0 | -M | -2M | ) |
Ec. Z MOD | ( | 1 | -5-2M | -12+M | -4-3M | 0 | 0 | -2M | ) |

BAS | Z | X₁ | X₂ | X₃ | S₁ | W₂ | SOL |
Z | 1 | -5-2M | -12+M | -4-3M | 0 | 0 | -2M |
S1 | 0| 1 | 2 | 1 | 1 | 0 | 5 |
W2 | 0 | 2 | -1 | 3 | 0 | 1 | 2 |
Z | 1 | -7/3 | -40/3 | 0 | 0 | 4/3+M | 8/3 |
S1 | 0 | 1/3 | 7/3 | 0 | 1 | -1/3 | 13/3 |
X2 | 0 | 2/3 | -1/3 | 1 | 0 | 1/3 | 2/3 |

Ec. Z = | ( | 1 | -5-2M | -12+M | -4-3M | 0 | 0 | -2M | ) |
PIV(4+3M) | ( | 0 | 8/3+2M | -4/3-M | 4+3M | 0 | 4/3+M | 8/3+2M | ) |
Nva Ec. Z= | ( | 1 | -7/3 | -40/3 | 0 | 0 | 4/3+M | 8/3 | ) |Ec. S1 = | ( | 0 | 1 | 2 | 1 | 1 | 0 | 5 | ) |
PIV(-1) | ( | 0 | -2/3 | 1/3 | -1 | 0 | -1/3 | -2/3 | ) |
Nva Ec. S1= | ( | 0 | 1/3 | 7/3 | 0 | 1 | -1/3 | 13/3 | ) |

BAS | Z | X₁ | X₂ | X₃ | S₁ | W₂ | SOL |
Z | 1 | 0 | -29/2 | 7/2 | 0 | 5/2+M | 5 |
S1 | 0 | 0 | 5/2 | -1/2 | 1 | -1/2 | 4 |
X2 | 0 | 1 | -1/2 | 3/2 | 0 | 1/2 | 1 |

Ec. Z = | ( | 1 | -7/3 | -40/3 | 0 | 0 | 4/3+M | 8/3| ) |
PIV(7/3) | ( | 0 | 7/3 | -7/6 | 7/2 | 0 | 7/6 | 7/3 | ) |
Nva Ec. Z= | ( | 1 | 0 | -29/2 | 7/2 | 0 | 5/2+M | 5 | ) |

Ec. S1 = | ( | 0 | 1/3 | 7/3 | 0 | 1 | -1/3 | 13/3 | ) |
PIV(-1/3) | ( | 0 | -1/3 | 1/6 | -1/2 | 0 | -1/6 | -1/3 | ) |
Nva Ec. S1= | ( | 0 | 0 | 5/2 | -1/2 | 1 | -1/2 | 4 | ) |

BAS | Z | X₁ | X₂ | X₃ | S1 | W2 | SOL | | |
Z | 1 | 0 | 0 | 3/5 | 29/5 |2.49+M | 5.11 | | |
X1 | 0 | 0 | 1 | -1/5 | 2/5 | -1/5 | 8/5 | | |
X2 | 0 | 1 | 0 | 7/5 | 1/5 | 2/5 | 9/5 | | |

Ec. Z = | ( | 1 | 0 | -29/2 | 7/2 | 0 | 5/2+M | 5 | ) |
PIV(29/2) | ( | 0 | 0 | 29/2 | -29/10 | 29/5 | -2/145 | 16/145 | ) |
Nva Ec. Z= | ( | 1 | 0 | 0 | 3/5 | 29/5 | 2.49+M | 5.11 | ) |

Ec. X2 = | ( | 0 | 1 | -1/2 | 3/2 | 0 | 1/2 | 1 | ) |
PIV(1/2) | ( | 0 | 0 | 1/2 |-1/10 | 1/5 | -1/10 | 4/5 | ) |
Nva Ec. X1= | ( | 0 | 1 | 0 | 7/5 | 1/5 | 2/5 | 9/5 | ) |

42.

Max Z=2x1+4x2+4x3-3x4
Sujeto a: x1+x2+x3=4
x1+4x2+x4=8
x1,x2,x3,x4≥0

Max Z=2x1+4x2+4x3-3x4
Sujeto a: x1+x2+x3=4
x1+4x2+x4=8
x1,x2,x3,x4≥0

Max Z=2x1+4x2+4x3-3x4-MW1-MW2
Sujeto a: x1+x2+x3+W1=4
x1+4x2+x4+W2=8
x1,x2,x3,x4≥0

| | | | | | | | | | |
| Básicas | Z | X1 |X2 | X3 | X4 | W1 | W2 | Solución | |
| Z | 1 | -2 | -4 | -4 | 3 | M | M | 0 | |
| W1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 4 | |
| W2 | 0 | 1 | 4 | 0 | 1 | 0 | 1 | 8 | |
| | | | | | | | | | |

Ecuación Z | 1 | -2 | -4 | -4 | 3 | M | M | 0 |
W1*(-M) | 0 | -M | -M | -M | 0 | -M | 0 | -4M |
W2*(-M) | 0 | -M | -4M | 0 | -M | 0 | -M | -8M |
Nueva Ecuacion Z | 1 | -2M-2 |-5M-4 | -M-4 | -M+3 | 0 | 0 | -12M |

| | | | ↓ | | | | | | |
| Básicas | Z | X1 | X2 | X3 | X4 | W1 | W2 | Solución | |
| Z | 1 | -2M-2 | -5M-4 | -M-4 | -M+3 | 0 | 0 | -12M | |
| W1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 4 | 4/1=4 |
← | W2 | 0 | 1 | 4 | 0 | 1 | 0 | 1 | 8 | 8/4=2 |
| | | | | | | | | | |

| | | | | ↓ | | | | | |
| Básicas | Z | X1 | X2 |X3 | X4 | W1 | W2 | Solución | |
| Z | 1 | -2M-2 | -5M-4 | -M-4 | -M+3 | 0 | 0 | -2M+8 | |
← | W1 | 0 | 3/4 | 0 | 1 | -1/4 | 1 | -1/4 | 2 | 2/1=2 |
| X2 | 0 | 1/4 | 1 | 0 | 1/4 | 0 | 1/4 | 2 | 2/0=no |
| | | | | | | | | | |

| | | | | | | | | | |
| Básicas | Z | X1 | X2 | X3 | X4 | W1 | W2 | Solución | |
| Z | 1 | 2 | 0 | 0 | 3 | M+4 | M-1/3 | 16 | |...