DEBER º 5

NOMBRE: Carolina SantillánSEMESTRE: Quinto “A”FECHA: 27/10/14TEMA: EJERCICIOS DE MAXIMIZACIÓN POR EL MÉTODO SIMPLEX

1.- MAXIMIZAR: 5 X1 + 3 X2 + 2 X32 X1 + 3 X2 + 5 X3 ≤ 52 X1 + 5 X2 + 3 X3 ≤ 125 X1 + 3 X2 + 7 X3 ≤ 202 X1 -2 X2 -3 X3 ≤ 12X1, X2, X3 ≥ 0

MAXIMIZAR: 5 X1 + 3 X2 + 2 X3 + 0 X4 + 0 X5 + 0 X6 + 0 X72 X1 + 3 X2 + 5 X3 + 1 X4 = 52 X1 + 5 X2 + 3 X3 + 1 X5 = 125 X1 + 3 X2 + 7 X3 + 1 X6 = 202 X1 -2 X2 -3 X3 + 1 X7 = 12X1, X2, X3, X4, X5, X6, X7 ≥ 0

Tabla 1 5 3 2 0 0 0 0

Base Cb

P0 P1 P2 P3 P4P5

P6 P7

P4 0 5 2 3 5 1 0 0 0

P5 0 12 2 5 3 0 1 0 0

P6 0 20 5 3 7 0 0 1 0

P7 0 12 2 -2 -3 0 0 0 1

Z 0 -5 -3 -2 0 0 0 0

Tabla 2

5 3 2 0 0 0 0

Base Cb P0 P1 P2 P3 P4 P5 P6 P7

P1 5 2.5 1 1.5 2.5 0.5 0 0 0

P5 0 7 0 2 -2 -1 1 0 0

P6 0 7.5 0-

4.5-5.5 -2.5 0 1 0

P7 0 7 0 -5 -8 -1 0 0 1

Z 12.5 0 4.5 10.5 2.5 0 0 0

La solución óptima es Z = 12.5X1 = 2.5X2 = 0X3 = 0

EJERCICIO 2MAXIMIZAR: 4 X1 + 2 X2 + 8 X3 + 3 X42 X1 + 5 X2 + 7 X3 + 8 X4 ≤ 235 X1 + 7 X2 + 5 X3 + 8 X4 ≤ 46 X1 + 3 X2 -2 X3 + 5 X4 ≤ 42 X1 -4 X2 -3 X3 + 2 X4 ≤ 12X1, X2, X3, X4 ≥ 0

MAXIMIZAR: 4 X1 + 2 X2 + 8 X3 + 3 X4 + 0 X5 + 0 X6 + 0 X7 + 0 X82 X1 + 5 X2 + 7 X3 + 8 X4 + 1 X5 = 235 X1 + 7 X2 + 5 X3 + 8 X4 + 1 X6 = 46 X1 + 3 X2 -2 X3 + 5 X4 + 1 X7 = 42 X1 -4 X2 -3 X3 + 2 X4 + 1 X8 = 12X1, X2, X3, X4, X5, X6, X7, X8 ≥ 0

Tabla 2 4 2 8 3 0 0 0 0

Base Cb P0 P1 P2 P3 P4 P5 P6 P7 P8

P5 0 17.4 -5 -4.8 0 -3.2 1-

1.40 0

P3 8 0.8 1 1.4 1 1.6 0 0.2 0 0

P7 0 5.6 8 5.8 0 8.2 0 0.4 1 0

P8 0 14.4 5 0.2 0 6.8 0 0.6 0 1

Tabla 1

4 2 8 3 0 0 0 0

Base Cb P0 P1 P2 P3 P4 P5 P6 P7 P8

P5 0 23 2 5 7 8 1 0 0 0

P6 0 4 5 7 5 8 0 1 0 0

P7 0 4 6 3 -2 5 0 0 1 0

P8 0 12 2 -4 -3 2 0 0 0 1

Z 0 -4 -2 -8 -3 0 0 0 0

Z 6.4 4 9.2 0 9.8 0 1.6 0 0La solución óptima es Z = 6.4X1 = 0X2 = 0X3 = 0.8X4 = 0