-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

-3 X1 -4 Y2 +MA1 - 0H1- 0H2- 0H3-2M1 - MA1 +M = -5M

(-2M-3)XI – 4 M = -5M

0 X1 + 3 X2 + h3 = 12X1, X2, A1,HI,H2,H3≥ 0

VB Cb TOTAL X1

Y2 H1 H2 H3

P4 0 11 0 4 1 1 0

X1 3 8 1 2 1 / 2 0 0

P5 0 12 0 3 0 0 1

Z 24 0 2 3 / 2 0 0

La solución óptima es Z = 24X1 = 8X2 = 0