Metodo simplex

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Minimizar:
Z = 3x1 + 6x2
Sujeto a 4 X1 + x2 ≥ 20 X1 + x2 ≤ 20 X1 + x2 ≥ 10
Restricciones x1, x2 ≥ 0
Cambiar
4X1 + x2 – E1 + A1 = 20
X1 + x2 + H1 = 20
X1 + x2 - E2 + A2 = 10
Zmin. = 3x1 + 6x2 + (0) H + (0) E1 + (0) E2 + MA1 +MA2
Z - 3x1 - 6x2 + (0) H + (0) E1 + (0) E2 - MA1 +MA2 = 0
M = 3 ecuaciones N = 7 variables N – M = 4 variables no básicas
Columna que saleColumna que entra Pivote

| | X1 | X2 | H | E1 | E2 | A1 | A2 | Z | b |
1 | A1 | 4 | 1 | 0 | -1 | 0 | 1 | 0 | 0 | 20 |
2 | H | 1 | 1 | 1 | 0 | 0 | 0 | 0| 0 | 20 |
3 | A2 | 1 | 1 | 0 | 0 | -1 | 0 | 1 | 0 | 10 |
4 | Z | -3 | -6 | 0 | 0 | 0 | -m | -m | 1 | 0 |
| | | | | | | | | | |
5 | A1 | 4 | 1 | 0 | -1 | 0 | 1 | 0 | 0 | 20|
6 | H | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 20 |
7 | A2 | 1 | 1 | 0 | 0 | -1 | 0 | 1 | 0 | 10 |
8 | Z | 4m-3 | m-6 | 0 | -m | 0 | 0 | -m | 1 | 20m |
| | | | | | | | | | |
9| A1 | 4 | 1 | 0 | -1 | 0 | 1 | 0 | 0 | 20 |
10 | H | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 20 |
11 | A2 | 1 | 1 | 0 | 0 | -1 | 0 | 1 | 0 | 10 |
12 | Z | 5m-3 | 2m-6 | 0 | -m | -m | 0 | 0 | 1| 30m |
| | | | | | | | | | |
13 | A1 | 1 | ¼ | 0 | -1/4 | 0 | 1/4 | 0 | 10 | 5 |
14 | H | 0 | ¾ | 1 | ¼ | 0 | -1/4 | 0 | 0 | 15 |
15 | A2 | 0 | ¾ | 0 | ¼ | -1 | -1/4 | 1 |0 | 5 |
16 | Z | 0 | 3/4m-21/4 | 0 | 1/4m-3/4 | -m | -5/4+3/4 | 0 | 1 | 5m+15 |
17 | A1 | 1 | 0 | 0 | -1/3 | 1/3 | 1/3 | -1/3 | 0 | 10/3 |
18 | H | 0 | 0 | 1 | 0 | 1 | 0 | -1 | 0 | 10 |19 | A2 | 0 | 1 | 0 | 1/3 | -4/3 | -1/3 | 4/3 | 0 | 20/3 |
20 | Z | 0 | 0 | 0 | 1 | -7 | -m-1 | -m+7 | 1 | 50 |
| | X1 | X2 | H | E1 | E2 | A1 | A2 | Z | b |
17 | A1 | 1 | 1 | 0 | 0| -1 | 0 | 1 | 0 | 10 |
18 | H | 0 | 0 | 1 | 0 | 1 | 0 | -1 | 0 | 10 |
19 | A2 | 0 | 3 | 0 | 1 | -4 | -1 | 4 | 0 | 20 |
20 | Z | 0 | -3 | 0 | 0 | -3 | -m | -m+3 | 1 | 30 |
TABLA ÓPTIMA
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