Balanceo de lineas

Resuelve los siguientes ejercicios.

a) Maximizar z = 2x1 + 3x2
Sujeto a - x1 + x2 ≤ 5
X1 + x2 ≤ 8X1 - 2x2 ≤ 3
X1, x2 ≥0

- x1 + x2 +X3=5
X1 + x2 +X4= 8
X1 - 2x2 + X5=3
X1, x2 ≥0

Z-2x1-3x2=0
| | | | | | | | |
|   | X1 | X2 | X3 |X4 | X5 | Solución | |
| z | -2 | -3 | 0 | 0 | 0 | 0 | |
| x3 | -1 | 1 | 1 | 0 | 0 | 5 | |
| x4 | 1 | 1 | 0 | 1 | 0 | 8 | |
| x5 | 1 | -2 | 0 | 0 | 1 | 3 | |
| | | | | | | ||
|   | X1 | X2 | X3 | X4 | X5 | Solución | |
| z | -5 | 0 | 3 | 0 | 0 | 15 | |
| x2 | -1 | 1 | 1 | 0 | 0 | 5 | |
| x4 | 2 | 0 | -1 | 1 | 0 | 3 | |
| x5 | -1 | 0 | 2 | 0 | 1 | 7| |
| | | | | | | | |
|   | X1 | X2 | X3 | X4 | X5 | Solución | |
| z | 0 | 0 | 1 1/2 | 2 1/2 | 0 | 22 1/2 | |
| x2 | 0 | 1 | 1/2 | 1/2 | 0 | 6 1/2 | |
| x1 | 1 | 0 | -1/2 | 1/2 | 0 | 1 1/2 | |
| x5 | 0 | 0 | 1 1/2 | 1/2 | 1 | 8 1/2 | |
| | | | | | | | |
| z=45/2 | x4=0 | | | | | | |
| x1=3/2 | x3=0 | | | | | | |
| x2=13/2 | || | | | | |
| x5=17/2 | | | | | | | |
| | | | | | | | |

b) Minimizar z = 4x1 - x2 - 2x3
Sujeto a x1 + x2 ≤ 52 x1 + x2 ≤ 7
2x2 + x3 ≥ 6
X2 + x3 ≤ 4
X1, x2, x3 ≥0X1 + x2 + x4 = 5
2 x1 + x2 +x5= 7
2x2 + x3 –x6 + R1= 6X2 + x3 +x7= 4

Despeja
R1=6-2X2-X3+X6
Z=4X1-X2-2X3+M (6-2X2-X3+X6)
4X1-X2-2X3+6M-2MX2-MX3+MX6
Z=X1(4)+X2(-1-2M)+X3(-2-M)+MX6+6M
Z=-X1(4)-X2(-1-2M)-X3(-2-M)-MX6=6M
Z-(4)...