Ejercicio de Ejemplo

Max Z = 5x1 + 4x2 Z - 5x1 - 4x2 = 0

s.a. s.a.6x1 + 4x2 <= 24 6x1 + 4x2 + S1 = 24x1 + 2x2 <= 6 x1 + 2x2 + S2 = 6-X1 + X2 <= 1 -X1 + X2 + S3 = 1x2 <= 2 x2 + S4 = 2

x1, x2 >= 0 x1, x2 >= 0

Básica Z X1 X2 S1 S2 S3 S4 Solución

Z 1 -5 -4 0 0 0 0 0S1 0 6 4 1 0 0 0 24S2 0 1 2 0 1 0 0 6S3 0 -1 1 0 0 1 0 1S4 0 0 1 0 0 0 1 2

Básica Z X1 X2 S1 S2 S3 S4 Solución Z 1 0 -0.67 0.83 0 0 0 20

X1 0 1 0.67 0.17 0 0 0 4S2 0 0 1.33 -0.17 1 0 0 2S3 0 0 1.67 0.17 0 1 0 5S4 0 0 1 0 0 0 1 2

Básica Z X1 X2 S1 S2 S3 S4 Solución Z 1 0 0 0.75 0.5 0 0 21

X1 0 1 0 0.25 -0.5 0 0 3.0X2 0 0 1 -0.125 0.75 0 0 1.5S3 0 0 0 0.375 -1.25 1 0 2.5S4 0 0 0 0.125 -0.75 0 1 0.5

2.- Todos los demás renglones, inclusive z:Nuevo renglón = (Renglón actual) – (Su coeficiente de la columna pivote) * (Nuevo reglón pivote).

4

6

-1

#DIV/0!

6

1.5

3

2

2.- Todos los demás renglones, inclusive z:Nuevo renglón = (Renglón actual) – (Su coeficiente de la columna pivote) * (Nuevo reglón pivote).

Ejercicio 2

Max z = 3x1 + x2 + 3x3 + 2x4 Max z - 3x1 - x2 - 3x3 - 2x4s.a. s.a.

x1 <= 5x1 + x2 + x3 + x4 <= 125x3 - x4 <= 253x2 + x3 <= 10-4x3 + 4x4 <= 5

x1, x2, x3, x4 >=0 x1, x2, x3, x4 >=0

PRIMERA ITERACION

Básica Z X1 X2 X3 X4 S1 S2Z 1 -3 -1 -3 -2 0 0

S1 0 1 0 0 0 1 0S2 0 1 1 1 1 0 1S3 0 0 0 5 -1 0 0S4 0 0 3 1 0 0 0S5 0 0 0 -4 4 0 0

SEGUNDA ITERACION

Básica Z X1 X2 X3 X4 S1 S2Z 1 -3 -1 0 -2.6 0 0

S1 0 1 0 0 0 1 0S2 0 1 1 0 1.2 0 1X3 0 0 0 1 -0.2 0 0S4 0 0 3 0 0.2 0 0S5 0 0 0 0 3.2 0 0

SEGUNDA ITERACION

Básica Z X1 X2 X3 X4 S1 S2Z 1 0 -1 0 -2.6 3 0

X1 0 1 0 0 0 1 0S2 0 0 1 0 1.2 -1 1X3 0 0 0 1 -0.2 0 0S4 0 0 3 0 0.2 0 0S5 0 0 0 0 3.2 0 0

Básica Z X1 X2 X3 X4 S1 S2

Z 1 0 1.166667 0 0 0.833333 2.166667X1 0 1 0 0 0 1 0X4 0 0 0.833333 0 1 -0.833333 0.833333X3 0 0 0.166667 1 0 -0.166667 0.166667S4 0 0 2.833333 0 0 0.166667 -0.166667S5 0 0 -2.666667 0 0 2.666667 -2.666667

SOLUCION:

Z = 34.33333X1 = 5X2 = 0X3 = 5.333333X4 = 1.666667

Max z - 3x1 - x2 - 3x3 - 2x4s.a.

x1 + s1 = 5x1 + x2 + x3 + x4 + s2 = 125x3 - x4 + s3 = 253x2 + x3 + s4 = 10-4x3 + 4x4 + s5 = 5

x1, x2, x3, x4 >=0

S3 S4 S5 Solución 0 0 0 00 0 0 5 #DIV/0!

0 0 0 12 12

1 0 0 25 5

0 1 0 10 10

0 0 0 5 -1.25

S3 S4 S5 Solución 0.6 0 0 150 0 0 5 5

-0.2 0 0 7 70.2 0 0 5 #DIV/0!-0.2 1 0 5 #DIV/0!0.8 0 0 25 #DIV/0!

S3 S4 S5 Solución 0.6 0 0 300 0 0 5 #DIV/0!

-0.2 0 0 2 1.66666670.2 0 0 5 -25-0.2 1 0 5 250.8 0 0 25 7.8125

S3 S4 S5 Solución

0.166667 0 0 34.33333330 0 0 5

-0.166667 0 0 1.666666670.166667 0 0 5.33333333-0.166667 1 0 4.666666671.333333 0 0 19.6666667