Método de la doble fase

METODO DE LA DOBLE FASE
MAX Z= 25X1 + 50X2 + 110X3
SA X1 + 2X2 + 4X3 ≤ 7200 MIN
120X1 + 200 X2 + 360X3 ≤ 3 000 000 GR
X1 ≤ 3000 ENVASES
X2 ≤ 2000 ENVASES
X3 ≤ 1500ENVASES
X2 ≥ 300 ENVASES = VENTA COMPROMETIDA
MINIMIZAR Z= S1
Z – S1 = 0
SA X1 + 2X2 + 4X3 + X4 = 7200
120X1 + 200X2 + 360X3 + X5 = 3000000
X1 + X6 = 3000
X2 + X7 =2000
X3 + X8 = 1500
X2 – X9 + S1 = 300
X1, X2, X3, X4, X5, X6, X7, X8, X9, S1 ≥ 0
X1 X2 X3 X4 X5 X6 X7 X8 X9 S1 RES
Z 0 0 0 0 0 0 0 0 0 -1 0
X4 1 2 4 1 0 0 0 0 0 0 7200
X5 120 200 360 0 1 0 0 00 0 3000000
X6 1 0 0 0 0 1 0 0 0 0 3000
X7 0 1 0 0 0 0 1 0 0 0 2000
X8 0 0 1 0 0 0 0 1 0 0 1500
S1 0 1 0 0 0 0 0 0 -1 1 300

CONVERTIR S1 EN CERO F1 + F7


X1 X2
X3 X4 X5 X6 X7 X8 X9 S1RES
Z 0 1 0 0 0 0 0 0 -1 0 300
X4 1 2 4 1 0 0 0 0 0 0 7200
X5 120 200 360 0 1 0 0 0 0 0 3000000
X6 1 0 0 0 0 1 0 0 0 0 3000
X7 0 1 0 0 0 0 1 0 0 0 2000
X8 0 0 1 0 0 0 0 1 0 0 1500
S1 0 1 0 0 0 00 0 -1 1 300

X4 = 7200/2 = 3600
X5 = 3000000/200 = 15000
X6 = 3000/0 = ∞
X7 = 2000/1 = 2000
X8 = 1500/0 = ∞
S1 = 300/1 = 300

X1 X2 X3 X4 X5 X6 X7 X8 X9 S1 RES
Z 0 0 0 0 0 0 0 0 0 -1 0
X41 0 4 1 0 0 0 0 2 -2 6600
X5 120 0 360 0 1 0 0 0 200 -200 2940000
X6 1 0 0 0 0 1 0 0 0 0 3000
X7 0 0 0 0 0 0 1 0 1 -1 1700
X8 0 0 1 0 0 0 0 1 0 0 1500
X2 0 1 0 0 0 0 0 0 -1 1 300

F5 – F7
F3– 200 F7
F2 – 2F7
F1 – F7




FASE II
X1 X2 X3 X4 X5 X6 X7 X8 X9 RES
Z -25 -50 -110 0 0 0 0 0 0 0
X4 1 0 4 1 0 0 0 0 2 6600
X5 120 0 360 0 1 0 0 0 200 2940000
X6 1 0 0 0 0 1 0 0 0 3000
X70 0 0 0 0 0 1 0 1 1700
X8 0 0 1 0 0 0 0 1 0 1500
X2 0 1 0 0 0 0 0 0 -1 300

(VARIABLES BASICAS EN FUNCION OBJETIVO)
PRIMERO CONVERTIR X2 EN CERO F1 + 50 F7
X1 X2 X3 X4 X5 X6 X7 X8 X9 RES
Z-25 0 -110 0 0 0 0 0 0 0
X4 1 0 4 1 0 0 0 0 2 6600
X5 120 0 360 0 1 0 0 0 200 2940000
X6 1 0 0 0 0 1 0 0 0 3000
X7 0 0 0 0 0 0 1 0 1 1700
X8 0 0 1 0 0 0 0 1 0 1500
X2 0 1 0 0 0 0 0 0 -1 300...