Practica 3
9
ESTANDARIZADO MAX 12x1+5x2+15x3+10x4+0S1+0S2+0S3+0S4+0S5+0S6+0S7-Ma1-Ma ST x1+x2+9x3+12x4+S1=1500 2x1+3x2+4x3+x4+S2=1000 x1+2x2+5x3+10x4+S3=800 X1-S4+a1=40 X2-S5+a2=130 X3-S6+a3=30 X4+S7=10 PRIMERO: VARIABLES DE DECISIÓN V.B X1 X2 X3 X4 S1 S1 5 1 9 12 1 S2 2 3 4 1 0 S3 3 2 5 10 0 a1 1 0 0 0 0 a2 0 1 0 0 0 a3 0 0 1 0 0 S7 0 0 0 1 0 Z -12 -5 -15 -10 0 -9 S1 5 1 5 12 1 -4 S2 2 3 0 1 0 -5 S3 3 2 0 10 0 0 a1 1 0 0 0 0 0 a2 0 1 0 0 0 -1 X3 0 0 1 0 0 0 S7 0 0 0 1 0 15 Z -12 -5 0 -10 0 -5 S1 0 1 5 12 1 -2 S2 0 3 0 1 0 -3 S3 0 2 0 10 0 -1 X1 1 0 0 0 0 0 a2 0 1 0 0 0 0 X3 0 0 1 0 0 0 S7 0 0 0 1 0 12 Z 0 -5 0 -10 0 -12 S1 0 1 5 0 1 -1 S2 0 3 0 0 0 -10 S3 0 2 0 0 0 0 X1 1 0 0 0 0 0 a2 0 1 0 0 0 0 X3 0 0 1 0 0
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INVESTIGACIÓN DE OPERACIONES
Transcript of Practica 3
ESTANDARIZADOMAX 12x1+5x2+15x3+10x4+0S1+0S2+0S3+0S4+0S5+0S6+0S7-Ma1-Ma2-Ma3ST
5x1+x2+9x3+12x4+S1=1500 2x1+3x2+4x3+x4+S2=1000
3x1+2x2+5x3+10x4+S3=800 X1-S4+a1=40
X2-S5+a2=130X3-S6+a3=30
X4+S7=10
PRIMERO:VARIABLES DE DECISIÓN VARIABLES DE HOLGURA
V.B X1 X2 X3 X4 S1 S2S1 5 1 9 12 1 0S2 2 3 4 1 0 1S3 3 2 5 10 0 0a1 1 0 0 0 0 0a2 0 1 0 0 0 0a3 0 0 1 0 0 0S7 0 0 0 1 0 0
Z -12 -5 -15 -10 0 0-9 S1 5 1 5 12 1 0-4 S2 2 3 0 1 0 1-5 S3 3 2 0 10 0 00 a1 1 0 0 0 0 00 a2 0 1 0 0 0 0
-1 X3 0 0 1 0 0 00 S7 0 0 0 1 0 0
15 Z -12 -5 0 -10 0 0-5 S1 0 1 5 12 1 0-2 S2 0 3 0 1 0 1-3 S3 0 2 0 10 0 0-1 X1 1 0 0 0 0 00 a2 0 1 0 0 0 00 X3 0 0 1 0 0 00 S7 0 0 0 1 0 0
12 Z 0 -5 0 -10 0 0-12 S1 0 1 5 0 1 0
-1 S2 0 3 0 0 0 1-10 S3 0 2 0 0 0 0
0 X1 1 0 0 0 0 00 a2 0 1 0 0 0 00 X3 0 0 1 0 0 0
-1 X4 0 0 0 1 0 010 Z 0 -5 0 0 0 0-1 S1 0 0 5 0 1 0-3 S2 0 0 0 0 0 1-2 S3 0 0 0 0 0 00 X1 1 0 0 0 0 0
-1 X2 0 1 0 0 0 00 X3 0 0 1 0 0 00 X4 0 0 0 1 0 05 Z 0 0 0 0 0 0
-4 S1 0 0 5 0 1 0-4 S2 0 0 0 0 0 1-5 S6 0 0 0 0 0 00 X1 1 0 0 0 0 00 X2 0 1 0 0 0 01 X3 0 0 1 0 0 00 S7 0 0 0 1 0 0
15 Z 0 0 0 0 0 04 S1 0 0 5 4 1 0
-7 S2 0 0 0 -7 0 12 S4 0 0 0 2 0 00 X1 1 0 0 0 0 00 X2 0 1 0 0 0 02 X3 0 0 1 2 0 0
-1 X4 0 0 0 1 0 020 Z 0 0 0 20 0 0
-2.6 S1 0 0 5 -4.66666667 1 00.4 S2 0 0 0 -5.66666667 0 1
-0.6 S4 0 0 0 3.33333333 0 01 X1 1 0 0 3.33333333 0 00 X2 0 1 0 0 0 0
-0.6 X3 0 0 1 0 0 00 X4 0 0 0 1 0 03 Z 0 0 0 30 0 0
RESPUESTA:
LA SOLUCIÓN ÓPTIMA ES:
X1= 130X2= 130X3= 30X4= 10Z= 2660
FILA/COLUMNA PIVOTPIVOT
EX FILA PIVOTRESPUESTA
VARIABLES DE HOLGURA VARIABLES ARTIFICIALES
S3 S4 S5 S6 S7 a1 a2 a30 0 0 0 0 0 0 00 0 0 0 0 0 0 01 0 0 0 0 0 0 00 -1 0 0 0 1 0 00 0 -1 0 0 0 1 00 0 0 -1 0 0 0 10 0 0 0 1 0 0 00 0 0 0 0 1000 1000 10000 0 0 4 0 0 0 -40 0 0 4 0 0 0 -41 0 0 5 0 0 0 -50 -1 0 0 0 1 0 00 0 -1 0 0 0 1 00 0 0 -1 0 0 0 10 0 0 0 1 0 0 00 0 0 -15 0 1000 1000 10150 5 0 4 0 -5 0 -40 2 0 4 0 -2 0 -41 3 0 5 0 -3 0 -50 -1 0 0 0 1 0 00 0 -1 0 0 0 1 00 0 0 -1 0 0 0 10 0 0 0 1 0 0 00 -12 0 -15 0 1012 1000 10150 5 0 4 -12 -5 0 -40 2 0 4 -1 -2 0 -41 3 0 5 -10 -3 0 -50 -1 0 0 0 1 0 00 0 -1 0 0 0 1 00 0 0 -1 0 0 0 1
0 0 0 0 1 0 0 00 -12 0 -15 10 1012 1000 10150 5 1 4 -12 -5 -1 -40 2 3 4 -1 -2 -3 -41 3 2 5 -10 -3 -2 -50 -1 0 0 0 1 0 00 0 -1 0 0 0 1 00 0 0 -1 0 0 0 10 0 0 0 1 0 0 00 -12 -5 -15 10 1012 1005 1015
-0.8 2.6 -0.6 0 -4 -2.6 0.6 0-0.8 -0.4 1.4 0 7 0.4 -1.4 00.2 0.6 0.4 1 -2 -0.6 -0.4 -1
0 -1 0 0 0 1 0 00 0 -1 0 0 0 1 0
0.2 0.6 0.4 0 -2 -0.6 -0.4 00 0 0 0 1 0 0 03 -3 1 0 -20 1003 999 1000
-0.8 2.6 -0.6 0 0 -2.6 0.6 0-0.8 -0.4 1.4 0 0 0.4 -1.4 00.2 0.6 0.4 1 0 -0.6 -0.4 -1
0 -1 0 0 0 1 0 00 0 -1 0 0 0 1 0
0.2 0.6 0.4 0 0 -0.6 -0.4 00 0 0 0 1 0 0 03 -3 1 0 0 1003 999 1000
-1.66666667 0 -2.33333333 -4.33333333 0 0 2.33333333 4.33333333-0.66666667 0 1.66666667 0.66666667 0 0 -1.66666667 -0.666666670.33333333 1 0.66666667 1.66666667 0 -1 -0.66666667 -1.666666670.33333333 0 0.66666667 1.66666667 0 0 -0.66666667 -1.66666667
0 0 -1 0 0 0 1 00 0 0 -1 0 0 0 10 0 0 0 1 0 0 04 0 3 5 0 1000 997 995
b Ɵ1500 166.66671000 250.0000
800 160.000040 INFINITO I
130 INFINITO30 30.000010 INFINITO
01380 276
880 440650 216.6666667
40 40 II130 INFINITO
30 INFINITO10 INFINITO
4501180 98.33333333
800 800530 53 III
40 INFINITO130 INFINITO
30 INFINITO10 10
9301060 1060
790 263.3333333430 215 IV
40 INFINITO130 130
30 INFINITO
10 INFINITO1030
930 232.5400 100170 34
40 INFINITO V130 INFINITO
30 -3010 INFINITO
1680794 -198.5264 37.71428571
34 -1740 INFINITO VI
130 INFINITO64 -3210 10
2190834 320.7692308194 -485
54 9040 -40 VII
130 INFINITO84 14010 INFINITO
2390600230
90 150130 VIII130
3010
2660
MIN Z=5A+8B+0S1+0S2+0S3-MA1-MA2-MA3 Reglas de aumentoST Tipo
4A+10B-S1+A1=40 Restricción10A+5B-S2+A2=50 <=7Q+7B-S3+A3=49 >=
=
Reglas de aumento en la F.O.
VariableAgregada
+Si -Si +Ai
VARIABLES DE DECISIÓN VARIABLES DE HOLGURA
VB A B S1 S2A1 4 10 -1 0A2 10 5 0 -1A3 7 7 0 0Z -5 -8 0 0
-4 A1 0 8 -1 0.4-10 A2 1 0.5 0 -0.1
-7 A 0 3.5 0 0.75 Z 0 -5.5 0 -0.5
-8 B 0 1 -0.125 0.05-0.5 A2 1 0 0.0625 -0.125-3.5 A 0 0 0.4375 0.5255.5 Z 0 0 -0.6875 -0.225
BA2A3Z
Reglas de aumentoVariablesagregadas
+Si Variable de holgura -Si +Ai Variable de exceso + Variable artificial
+Ai Variable artificial
Reglas de aumento en la F.O.
Funcion Objetivo * tiene infinitas soluciones*Max Min 0Si 0Si 0Si 0Si
-MAi +MAi
VARIABLES DE HOLGURA VARIABLES ARTIFICIALES
S3 A1 A2 A3 b Ɵ0 1 0 0 40 100 0 1 0 50 5 I
-1 0 0 1 49 70 1000 1000 1000 00 1 -0.4 0 20 2.50 0 0.1 0 5 10 II
-1 0 -0.7 1 14 40 1000 1000.5 1000 250 0.125 -0.05 0 2.5 500 -0.0625 0.125 0 3.75 -30 III
-1 -0.4375 -0.525 1 5.25 100 1000.6875 1000.225 1000 38.75
IV
