Minimizacion de modelos PL
Enviado por Alvaro LB • 27 de Abril de 2017 • Tarea • 254 Palabras (2 Páginas) • 104 Visitas
- Minz= .23x1+.85x2+.65x3
s.a .12x1+.75x2+.65x3>=700
.25x1+.15x2+.10x3>=1500
x1 + x2 + x3 >=1200
x1 , x2 , x3 >=0
Modelo Estándar
Minz= .23x1+.85x2+.65x3+0E1+MA1+0E2+MA2+0E3+MA3
s.a .12x1+.75x2+.65x3-E1+A1-0E2+0A2-0E3+0A3=700
.25x1+.75x2+.65x3-0E1+0A1-E2+A2-0E3+0A3=1500
x1 + x2 + x3 -0E1+0A1-0E2+0A2-E3+A3=1200
Tabla #1 | Cj | .23 | .85 | .65 | 0 | 0 | 0 | M | M | M | ||
Variables básicas | X1 | X2 | X3 | E1 | E2 | E3 | A1 | A2 | A3 | Valor | Ratio | |
A1 | M | .12 | .75 | .65 | -1 | 0 | 0 | 1 | 0 | 0 | 700 | 2800/3 |
A2 | M | .25 | .15 | .10 | 0 | -1 | 0 | 0 | 1 | 0 | 1500 | 10000 |
A3 | M | 1 | 1 | 1 | 0 | 0 | -1 | 0 | 0 | 1 | 1200 | 1200 |
Zj | 137/ 100M | 19/10M | 7/4M | -M | -M | -M | M | M | M | 3400M | ||
Cj-Zj | .23 – 137 /100M | .85 – 19/10M | .65 – 7/4M | M | M | M | M | 0 | 0 |
Tabla #2 | Cj | .23 | .85 | .65 | 0 | 0 | 0 | M | M | M | ||
Variables básicas | X1 | X2 | X3 | E1 | E2 | E3 | A1 | A2 | A3 | Valor | Ratio | |
X2 | .85 | 4/5 | 1 | 13/15 | -3/4 | 0 | 0 | 4/3 | 0 | 0 | 2800/3 | -700 |
A2 | M | 113 / 5000 | 0 | - 3/ 100 | 1/5 | -1 | 0 | -1/5 | 1 | 0 | 1360 | 6800 |
A3 | M | 21/25 | 0 | 2/5 | 4/3 | 0 | -1 | 0 | 0 | 1 | 800/3 | 200 |
Zj | 17/25 + 533/ 500M | .85 | 221/ 300+31/ 300M | -17/ 15 + 23/15M | -M | -M | 17/5 – 1/5M | M | M | 2380/3 + 4880/ 3M | ||
Cj-Zj | -9/20 – 533/ 500M | 0 | -13/ 150 – 31/ 300M | 17/ 15 – 23/ 15M | M | M | -17/5 + 6/M | 0 | 0 |
Tabla #3 | Cj | .23 | .85 | .65 | 0 | 0 | 0 | M | M | M | ||
Variables básicas | X1 | X2 | X3 | E1 | E2 | E3 | A1 | A2 | A3 | Valor | Ratio | |
X2 | .85 | 1 | 1 | 1 | -3/4 | 0 | -1 | 4/3 | 0 | 1 | 1200 | -1200 |
A2 | M | 1/10 | 0 | -1/20 | 1/5 | -1 | 3/20 | -1/5 | 1 | -3/20 | 1320 | 8800 |
E1 | 0 | 63/ 100 | 0 | 3/10 | 4/3 | 0 | -3/4 | 0 | 0 | 3/4 | 200 | -800/3 |
Zj | .85 + 1/10M | .85 | .85 – 1/2M | -17/15 + 23/15M | -M | -.85 | 17/5 – 1/5M | M | .85 – 3/20M | |||
Cj-Zj | -31/50 – 1/10M | 0 | -1/5 + 1/2M | 17/15 – 23/15M | M | M | -17/5 + 6/5M | 0 | -.85 + 23/20M |
Tabla #4 | Cj | .23 | .85 | .65 | 0 | 0 | 0 | M | M | M | ||
Variables básicas | X1 | X2 | X3 | E1 | E2 | E3 | A1 | A2 | A3 | Valor | Ratio | |
X2 | .85 | 5/3 | 1 | 2/3 | 0 | -20/3 | 0 | 0 | 20/3 | 0 | 10000 | 6000 |
E3 | 0 | 2/3 | 0 | -1/3 | 0 | -20/3 | 1 | -4/3 | 20/3 | -1 | 8800 | 1320 |
E1 | 0 | 113/ 100 | 0 | 1/20 | 1 | -5 | 0 | -1 | 5 | 0 | 6800 | 6017.70 |
Zj | 17/12 | .85 | 17/30 | 0 | -17/3 | 0 | 0 | 17/3 | 0 | 8500 | ||
Cj-Zj | -89/75 | 0 | 1/12 | 0 | 17/3 | 0 | M | M – 17/3 | 0 |
:. Tabla óptima
Tabla #5 | Cj | .23 | .85 | .65 | 0 | 0 | 0 | M | M | M | |
Variables básicas | X1 | X2 | X3 | E1 | E2 | E3 | A1 | A2 | A3 | Valor | |
X1 | .23 | 1 | 3/5 | 2/5 | 0 | -4 | 0 | 0 | 0 | 4 | 6000 |
E3 | 0 | 0 | -2/5 | -3/5 | 0 | -4 | 1 | -4/3 | 4 | -1 | 4800 |
E1 | 0 | 0 | -339/500 | -201/500 | 1 | -12/25 | 0 | -1 | 12/25 | 0 | 20 |
Zj | .23 | 69/500 | 23/250 | 0 | -23/25 | 0 | 0 | 0 | 23/25 | 1380 | |
Cj-Zj | 0 | 89/125 | 279/500 | 0 | 23/25 | 0 | M | M | M – 23/25 |
Solución óptima
X1=6000
E3=4800
E1=20
Z=1380
X2=x3=E2=A1=A2=A3=0
Comprobación de restricciones
Minz= .23x1+.85x2+.65x3+0E1+MA1+0E2+MA2+0E3+MA3
=.23(6000)+.85(0)+.65(0)+0(20)+1(0)+0(0)+1(0)+0(4800)+1(0)
=1380+0+0+0+0+0+0+0+0
=1380
R1= .12x1+.75x2+.65x3-E1+A1-0E2+0A2-0E3+0A3
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