Ejercicio con el metodo simplex
Enviado por Diana Marcela Campuzano Marquez • 9 de Noviembre de 2021 • Prácticas o problemas • 2.532 Palabras (11 Páginas) • 85 Visitas
UNIVERSIDAD COOPERATIVA DE COLOMBIA
PROGRAMACION LINEAL
METODO SIMPLEX
Resolver el siguiente ejercicio con el Método Simplex
MAX Z = 20X1 + 12X2[pic 1] - 15 X3 (0)
s.a: 5X1 - 3X2 [pic 2] 45 (1)
X1 + 6X3 [pic 3] 18 (2)
3X1 - 6X2[pic 4] + X3 [pic 5] 60 (3)
X1, X2, X3 [pic 6] 0
Solución:
Forma estándar: MAX Z - 20X1 - 12X[pic 7] +15X3 = 0 (0)
s.a: 5X[pic 8] - 3X2 + S1 = 45 (1)
X[pic 9] + 6X3 + S2 = 18 (2)
3X1 - 6X2[pic 10] + X3 +S3 = 60 (3
X[pic 11][pic 12] 0, S[pic 13][pic 14] 0
Forma Tabular:
VB | Z | X1 Entra | X2 | X3 | S1 | S2 | S3 | b[pic 15] | Sale |
Z | 1 | -20 | -12 | 15 | 0 | 0 | 0 | 0 | |
S1 | 0 | 5 | -3 | 0 | 1 | 0 | 0 | 45 | |
S2 | 0 | 1 | 0 | 6 | 0 | 1 | 0 | 18 | |
S3 | 0 | 3 | -6 | 1 | 0 | 0 | 1 | 60 | |
Z | 1 | 0 | -24 Entra | 15 | 4 | 0 | 0 | 180 | Sale |
X1 | 0 | 1 | -3/5 | 0 | 1/5 | 0 | 0 | 9 | |
S2 | 0 | 0 | 3/5 | 6 | -1/5 | 1 | 0 | 9 | |
S3 | 0 | 0 | -21/5 | 1 | -3/5 | 0 | 1 | 33 | |
Z | 1 | 0 | 0 | 255 | -4 | 40 | 0 | 540 | |
X[pic 16] | 0 | 1 | 0 | 6 | 0 | 1 | 0 | 18 | |
X[pic 17] | 0 | 0 | 1 | 10 | -1/3 | 5/3 | 0 | 15 | |
S3 | 0 | 0 | 0 | 43 | -2 | 7 | 1 | 96 |
OPERACIONES ITERACION 1:
NF[pic 18] = FV[pic 19] - CCP [NFP]
[-20 -12 15 0 0 0 0 ]
-(-20) [ 1 -3/5 0 [pic 20] 0 0 9 ]
...