Maximizar Z

Páginas: 4 (764 palabras) Publicado: 19 de octubre de 2012
Maximizar Z= 2X1 – X2 + X3
Sujeta a:
3X1 + X2 + X3 ≤ 6
X1 – X2 + 2X3 ≤ 1
X1 + X2 - X3 ≤ 2

YX1 ≧ 0, X2 ≧ 0, X3 ≧ 0

Forma Algebraica | Variable Básica | Ec.No. | | Lado derecho |
| | | Z | X1 | X2 | X3 | X4 | X5 | X6 | |
Z- 2X1 + X2 - X3 = 0 | Z | (0) |1 | -2 | 1 | -1 | 0 | 0 | 0 | 0 | |
3X1 + X2 + X3 + X4 = 6 | X4 | (1) | 0 | 3 | 1 | 1 | 1 | 0 | 0 | 6 | 2 |
X1 – X2 + 2X3 + X5 = 1 | X5 | (2) | 0 | 1 | -1 | 2| 0 | 1 | 0 | 1 | 1 |
X1 + X2 - X3 + X6 = 2 | X6 | (3) | 0 | 1 | 1 | -1 | 0 | 0 | 1 | 2 | 2 |
| Z | (0) | 1 | 0 | -1 | 3 | 0 | 2 | 0 | 2 | |
| X4 | (1) | 0 | 0 |4 | -5 | 1 | -3 | 0 | 3 | ¾ |
| X1 | (2) | 0 | 1 | -1 | 2 | 0 | 1 | 0 | 1 | --- |
| X6 | (3) | 0 | 0 | 2 | -3 | 0 | -1 | 1 | 1 | ½ |
(3/2,1/2,0,1,0,0) Z = 5/2 | Z | (0) | 1 | 0 | 0 | 3/2 | 0 |3/2 | 1/2 | 5/2 | |
| X4 | (1) | 0 | 0 | 0 | 1 | 1 | -1 | -2 | 1 | |
| X1 | (2) | 0 | 1 | 0 | 1/2 | 0 | 1/2 | 1/2 | 3/2 | |
| X2 | (3) | 0 | 0 | 1 | -3/2 | 0 | -1/2 | 1/2 | 1/2 | |Maximizar Z= 5X1 + X2 + 3X3 + 4X4
Sujeta a:
X1 – 2X2 + 4X3 + 3X4 ≤ 20
-4X1 + 6X2 + 5X3 - 4X4 ≤ 40
2X1 - 3X2+3X3 + 8X4 ≤ 50

Y X1 ≧ 0, X2 ≧ 0, X3 ≧ 0, X4 ≧ 0

Forma Algebraica | Variable Básica | Ec.No. | | Lado derecho |
| | | Z | X1 | X2 | X3 | X4 | X5 | X6 | X7 | |
Z - 5X1 - X2 - 3X3- 4X4 = 0 | Z | (0) | 1 | -5 | -1 | -3 | -4 | 0 | 0 | 0 | 0 | |
X1 – 2X2 + 4X3 + 3X4 + X5 = 20 | X5 | (1) | 0 | 1 | -2 | 4 | 3 | 1 | 0 | 0 | 20 | 20 |-4X1 + 6X2 + 5X3 - 4X4 +X6 = 40 | X6 | (2) | 0 | -4 | 6 | 5 | -4 | 0 | 1 | 0 | 40 | ----- |
2X1 - 3X2 +3X3 + 8X4 +X7 = 50 | X7 | (3) | 0 | 2 | -3 | 3 | 8 | 0 | 0 |...
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