Programacion Linial

Problema de mezcla
Solución
El modelo en programación lineal está dado por :

Z= 600x1+ 2.000x2+1.07x6+0S7+ 0S8-MA9-MA10-MA11-MA12
1. Igualamos las ecuaciones con la tabla del simplex.
1.1000x1+ 800x2+x3+A9=1500
2. 700x1-500 x2-1.07x3+x4+A10=500
3. -1.800x1+ 200x2-1.07x4+x5+A11=400
4. -400x1+ 700x2-1.07x5+x6+A12=380
5. x1+S7=1
6. x2+S8=1

x0,x1 ,x2 ,x4 ,x5,x6 ,s7,s8,A9,A10,A11,A12≥0
2. Construimos el modelo matemático en términos de x.
Z= 600x1+ 2.000x2+1.07x6+0x7+ 0x8-Mx9-Mx10-Mx11-Mx12

Sistemas de ecuaciones

1. 1000x1 + 800x2 +x3+ x9 =1500
2. 700x1 -500 x2-1.07x3+x4 +x10 =500
3. -1.800x1+ 200x2 -1.07x4+x5+x11 =400
4. -400x1 +700x2 -1.07x5+x6 +x12 =380
5. x1+x7 =1
6. x2 +x8 =1

∎Condicion deno negatividad

x1 , x2 ,x3 ,x4,x5,x6,x7,x8 ,x9 ,x10,x11 ,x12 ≥0

zj=cbaj

3. tabla de solucion inicial
| | | | | | | | | | | | | | |
| | | x1 | x2 | x3 | x4 | x5 | x6 |x7 | x8 | x9 | x10 | x11 | x12 |
| | cj | 600 | 2.000 | 0 | 0 | 0 | 1.07 | 0 | 0 | -M | -M | -M | -M |
cb | base | b | a1 | a2 | a3 | a4 | a5 | a6 | a7 | a8 | a9 | a10 | a11 | a12 |
-M | x9 |1500 | 1000 | 800 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
-M | x10 | 500 | 700 | -500 | -1.07 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
-M | x11 | 400 | -1.800 | 200 | 0 | -1.07 | 1 | 0 | 0 | 0 | 0 |0 | 1 | 0 |
-M | x12 | 380 | -400 | 700 | 0 | 0 | -1.07 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |
0 | x7 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | x8 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |...