resolución de ejercicios en el programa simplex
Post on 03-Aug-2015
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-2 X1 -1 X2 +MA1+ MA2- H1-H2-MX1 -MX2 - MA1 =-2M-2MX1 -3MX2 -MA2+M =-5M
(-3M-2)XI- 4M-1)X2 M -7M
RESOLUCIÓN DE EJERCICIOS EN EL PROGRAMA SIMPLEX
EJERCICIO 1
MAXIMIZAR: 2 X1 + 1 X21 X1 + 1 X2 = 22 X1 + 3 X2 ≥ 51 X1 + 2 X2 ≤ 3X1, X2 ≥ 0
MAXIMIZAR: 2 X1 + 1 X21 X1 + 1 X2 = 22 X1 + 3 X2 ≥ 51 X1 + 2 X2 ≤ 3X1, X2 ≥ 0
MAXIMIZAR: 2 X1 + 1 X2 - MA1- MA2+ H1+H21 X1 + 1 X2 + A1 = 22 X1 + 3 X2 –H1 + A2 = 51 X1 + 2 X2 + H2 = 3X1, X2, A1,A2,H1,H2 ≥ 0
La solución óptima es Z = 3X1 = 1X2 = 1
EJERCICIO 2
MAXIMIZAR: 3 X1 + 2 X21 X1 + 1 X2 ≤ 62 X1 -1 X2 ≥ 01 X1 + 0 X2 = 2
VB Z TOTAL X1
X2 H1 H2
H2 0 0 0 0 1 1
X1 2 1 1 0 1 0
X2 1 1 0 1 -1 0
Z 3 0 0 1 0
-3 X1 -2 X2 +MA1+ MA2- H1-H2-2M1 +MX2 - MA1 +M = 0-MX1 -MA2 =-2M
(-3M-3)XI +M-2)X2 M =-2M
X1, X2 ≥ 0MAXIMIZAR: 3 X1 + 2 X21 X1 + 1 X2 ≤ 62 X1 -1 X2 ≥ 01 X1 + 0 X2 = 2X1, X2 ≥ 0
MAXIMIZAR: 3 X1 + 2 X2 -MA1-MA2+H1+H21 X1 + 1 X2 + H1 = 62 X1 -1 X2 –H2 + A1 = 01 X1 + A2 = 2X1, X2, A1,A2,H1,H2≥ 0
VB CbTOTA
LX1
X2
H1 H2
H1 0 0 0 0 1 -1
X1 3 2 1 0 0 0
X2 2 4 0 1 0 1
Z 14 0 0 0 2
La solución óptima es Z = 14X1 = 2X2 = 4
EJERCICIO 3
MAXIMIZAR: 3 X1 + 4 X22 X1 + 4 X2 ≤ 162 X1 + 0 X2 ≥ 50 X1 + 3 X2 ≤ 12X1, X2 ≥ 0
MAXIMIZAR: 3 X1 + 4 X22 X1 + 4 X2 ≤ 162 X1 + 0 X2 ≥ 50 X1 + 3 X2 ≤ 12X1, X2 ≥ 0
MAXIMIZAR: 3 X1 + 4 X2 –MA1+0H1+0H2+0H32 X1 + 4 X2 + HI = 162 X1 –H2 +A1 = 5
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