Metodo simplex

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  • Publicado : 28 de mayo de 2010
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1.- Maximizar G = 4X1 +4X2

s.a. :
2X1 + 7X2 < 21
7X1 + 2X2 < 49
Xi > 0

FORMA ESTÁNDAR

Maximizar G = 4X1 +4X2 +0S1 + 0S2

2X1 + 7X2 + S1 = 21
7X1 + 2X2 + S2 = 49Xi > 0 i= 1,2
Si > 0 i= 1,2

MÉTODO SIMPLEX

TABLA BÁSICA INICIAL

Cj | 4 | 4 | 0 | 0 | Bi | Bi/xj |
CB | VB | X1 | X2 | S1 | S2 | | |
0 | S1 | 2 | 7 | 1 | 0 | 21 | 21/2 |
0 | S2 | 7 | 2 | 0 | 1 | 49 | 7 |
Zj | 0 | 0 | 0 | 0 | 0 |
Cj-Zj | 4 | 4 | 0 | 0 |

1ERA ITERACIÓN

Cj | 4 | 4 | 0 | 0 | Bi | Bi/xj |
CB | VB | X1 |X2 | S1 | S2 | | |
0 | S1 | 0 | 45/7 | 1 | -2 | 7 | 49/45 |
4 | X1 | 1 | 2/7 | 0 | 1/7 | 7 | 49/2 |
Zj | 4 | 8/7 | 0 | 4/7 | 28 |
Cj-Zj | 0 | 20/7 | 0 | -4/7 |

2DA ITERACIÓN: TABLA ÓPTIMA

Cj | 4 | 4 | 0 | 0 | Bi | Bi/xj |
CB | VB | X1 | X2 | S1 | S2 | | |
4 | X2 | 0 | 1 | 7/45 | -14/45 | 49/45 | |
4 | X1 | 1 | 0 | -2/45 | 73/315 | 301/45 | |
Zj | 4 | 4 | 4/9 | -20/63 |280/9 |
Cj-Zj | 0 | 0 | -4/9 | 20/63 |

SOLUCIÓN:

X1= 301/45 X2 = 49/45 S1 = 0 S2 = 0 Z= 280/9

COMPROBACIÓN:

2(301/45) + 7(49/45) = 21
7 (301/45) + 2 (49/45) = 49

____________________________________________________________

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2.- Maximizar G = 18X1 + 15X2

s.a:
2X1 + X2 < 500X1 < 150
X2 < 250
Xi > 0

FORMA ESTÁNDAR

Maximizar G = 18X1 +15X2 +0S1 + 0S2

2X1 + X2 + S1 = 500
X1 + S2 = 150
X2 + S3 = 250
Xi > 0 i=1,2
Si > 0 i= 1,2,3

MÉTODO SIMPLEX

TABLA BÁSICA INICIAL

Cj | 18 | 15 | 0 | 0 | 0 | Bi | Bi/xj |
CB | VB | X1 | X2 | S1 | S2 | S3 | | |
0 | S1 | 2 | 1 | 1 | 0 | 0 | 500 | 250 |
0 | S2 | 1 | 0 | 0 | 1 | 0 | 150 | 150 |
0 | S3 | 0 | 1 | 0 | 0 | 1 | 250 | - |
Zj | 0 | 0 | 0 | 0 | 0 | 0 |
Cj-Zj | 18 | 15 | 0 | 0 | 0 |

1ERA ITERACIÓNCj | 18 | 15 | 0 | 0 | 0 | Bi | Bi/xj |
CB | VB | X1 | X2 | S1 | S2 | S3 | | |
0 | S1 | 0 | 1 | 1 | -2 | 0 | 200 | 200 |
18 | X1 | 1 | 0 | 0 | 1 | 0 | 150 | - |
0 | S3 | 0 | 1 | 0 | 0 | 1 | 250 | 250 |
Zj | 18 | 0 | 0 | 18 | 0 | 2700 |
Cj-Zj | 0 | 15 | 0 | -18 | 0 |

2DA ITERACIÓN: TABLA ÓPTIMA

Cj | 18 | 15 | 0 | 0 | 0 | Bi | Bi/xj |
CB | VB | X1 | X2 | S1 | S2 | S3 | ||
15 | X2 | 0 | 1 | 1 | -2 | 0 | 200 | |
18 | x1 | 1 | 0 | 0 | 1 | 0 | 150 | |
0 | S3 | 0 | 0 | -1 | 2 | 1 | 50 | |
Zj | 18 | 15 | 15 | -12 | 0 | 5700 |
Cj-Zj | 0 | 0 | -15 | 12 | 0 |

SOLUCIÓN:

X1= 150 X2 = 200 S1 = 0 S2 = 0 S3 =50 Z= 5700

COMPROBACIÓN:

2(150) + 200 = 500
150 = 150
200 + 50 = 250

________________________________________________________________________

3.- Maximizar G = 3X1 + 4X2

s.a.:
3X1 + 5X2 < 300
10X1 + 15X2 < 750
15X2 < 250
10X1 + 10X2 < 600
Xi > 0

FORMA ESTÁNDAR

Maximizar G = 3X1 +4X2 +0S1 + 0S2 + 0S3 + 0S4

3X1 +5X2 + S1 = 300
10X1 + 15X2 + S2 = 750
15X2 + S3 = 250
10X1 + 10X2 + S4 = 600
Xi > 0 i= 1,2
Si > 0 i= 1,2,3,4

MÉTODO SIMPLEX

TABLA BÁSICA INICIAL

Cj | 3 | 4 | 0 | 0 | 0 | 0 | Bi | Bi/xj |
CB | VB | X1 | X2 | S1 | S2 | S3 | S4 | | |
0 | S1 | 3 | 5 | 1 | 0 | 0 | 0 | 300...
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