Ejercicio programacion lineal y no lineal

Ejercicio No. 1
Inicialmente, convertimos las restricciones a igualdades:
0,05 x1+ 0,05x2+ x3=1100
0,01 x1+ 0,05x2+ x4=1800
0,1 x1+ 0,05x2+ x5=2000
x1, x2, x3,x4,x5 ≥0
Función Objetivo:
Z =20x1 + 18.5x2
→ Z -20x1 – 18.5x2 = 0.

Tabla 1.
Base | Variable de Decisión | Variable de Holgura | Valor Solución | |
| x1 | x2 | x3 | x4 | x5 | | |
x3 | 0.05 | 0.05 | 1 | 0 | 0 |1100 | 22000 |
x4 | 0.01 | 0.05 | 0 | 1 | 0 | 1800 | 180000 |
x5 | 0.1 | 0.05 | 0 | 0 | 1 | 2000 | 20000 |
z | -20 | -18.5 | 0 | 0 | 0 | 0 | 0 |

Nueva Fila Pivote = Vieja Fila Pivote / PivoteNueva Fila Pivote: 1 0.5 0 0 10 20000

Coeficiente x3
0.05 | 0.05 | 1 | 0 | 0 | 1100 |
- | - | - | - | - | - |
0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 |
x | x | x | x | x | x |
1 | 0.5| 0 | 0 | 10 | 20000 |
= | = | = | = | = | = |
0 | 0.025 | 1 | 0 | -0.5 | 100 |

Coeficiente x4
0.01 | 0.05 | 0 | 1 | 0 | 1800 |
- | - | - | - | - | - |
0.01 | 0.01 | 0.01 | 0.01 | 0.01 |0.01 |
X | x | x | x | x | x |
1 | 0.5 | 0 | 0 | 10 | 20000 |
= | = | = | = | = | = |
0 | 0.045 | 0 | 1 | -0.1 | 1600 |

Z
-20 | -18.5 | 0 | 0 | 0 | 0 |
- | - | - | - | - | - |
-20 |-20 | -20 | -20 | -20 | -20 |
x | x | x | x | x | x |
1 | 0.5 | 0 | 0 | 10 | 20000 |
= | = | = | = | = | = |
0 | -8.5 | 0 | 0 | 200 | 400.000 |

Tabla 2.
Base | Variable de Decisión |Variable de Holgura | Valor Solución | |
| x1 | x2 | x3 | x4 | x5 | | 4000 |
x3 | 0 | 0.025 | 1 | 0 | -0.5 | 100 | 35555,5 |
x4 | 0 | 0.045 | 0 | -1 | 0.1 | 1600 | 40000 |
x1 | 1 | 0.5 | 0 | 0| 10 | 20000 | |
z | 0 | -8.5 | 0 | 0 | 200 | 400000 | |

Nueva Fila Pivote = Vieja Fila Pivote / Pivote
Nueva Fila Pivote: 0 1 40 0 20 4000
Coeficiente x4
0 | 0.045 | 0 | 1 | -0.1 | 1600 |- | - | - | - | - | - |
0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 |
X | x | x | x | x | x |
0 | 1 | 40 | 0 | 20 | 4000 |
= | = | = | = | = | = |
0 | 0 | -1.8 | 1 | -1 | 1420 |...