EJERCICIOS MÉTODO SIMPLEX

1. INVESTIGACIÓN OPERATIVA I
ABIAIL CRIOLLO
5TO SEMESTRE “A”
1
EJERCICIOS DE MAXIMIZACIÓN POR EL MÉTODO SIMPLEX
EJERCICIO 1
MAXIMIZAR: 7 X1 +
3 X2 + 2 X3
MAXIMIZAR: 7 X1 + 3 X2 + 2
X3 + 0 X4 + 0 X5 + 0 X6 + 0
X7
4 X1 + 5 X2 + 2 X3 ≤
10
3 X1 + 6 X2 + 3 X3 ≤
3
2 X1 + 9 X2 + 4 X3 ≤
12
3 X1 -2 X2 + 4 X3 ≤
20
4 X1 + 5 X2 + 2 X3 + 1 X4 =
10
3 X1 + 6 X2 + 3 X3 + 1 X5 = 3
2 X1 + 9 X2 + 4 X3 + 1 X6 =
12
3 X1 -2 X2 + 4 X3 + 1 X7 = 20
X1, X2, X3 ≥ 0 X1, X2, X3, X4, X5, X6, X7 ≥ 0
Tabla 1 7 3 2 0 0 0 0
Base Cb P0 P1 P2 P3 P4 P5 P6 P7
P4 0 10 4 5 2 1 0 0 0
P5 0 3 3 6 3 0 1 0 0
P6 0 12 2 9 4 0 0 1 0
P7 0 20 3 -2 4 0 0 0 1
Z 0 -7 -3 -2 0 0 0 0
Tabla 2 7 3 2 0 0 0 0
Base Cb P0 P1 P2 P3 P4 P5 P6 P7
P4 0 6 0 -3 -2 1 -1.3333333333333 0 0
P1 7 1 1 2 1 0 0.33333333333333 0 0
P6 0 10 0 5 2 0 -0.66666666666667 1 0

2. INVESTIGACIÓN OPERATIVA I
ABIAIL CRIOLLO
5TO SEMESTRE “A”
2
P7 0 17 0 -8 1 0 -1 0 1
Z 7 0 11 5 0 2.3333333333333 0 0
La solución óptima es Z = 7
X1 = 1
X2 = 0
X3 = 0
EJERCICIO 2
MAXIMIZAR: 4 X1 +
7 X2 + 3 X3 + 2 X4
MAXIMIZAR: 4 X1 + 7 X2 + 3
X3 + 2 X4 + 0 X5 + 0 X6 + 0
X7 + 0 X8
3 X1 + 4 X2 + 2 X3 +
8 X4 ≤ 12
4 X1 + 5 X2 + 8 X3 +
9 X4 ≤ 10
2 X1 + 2 X2 + 5 X3 +
7 X4 ≤ 12
9 X1 -5 X2 -3 X3 + 8
X4 ≤ 23
3 X1 + 4 X2 + 2 X3 + 8 X4 + 1
X5 = 12
4 X1 + 5 X2 + 8 X3 + 9 X4 + 1
X6 = 10
2 X1 + 2 X2 + 5 X3 + 7 X4 + 1
X7 = 12
9 X1 -5 X2 -3 X3 + 8 X4 + 1
X8 = 23
X1, X2, X3, X4 ≥ 0
X1, X2, X3, X4, X5, X6, X7,
X8 ≥ 0
Tabla 1 4 7 3 2 0 0 0 0
Base Cb P0 P1 P2 P3 P4 P5 P6 P7 P8
P5 0 12 3 4 2 8 1 0 0 0
P6 0 10 4 5 8 9 0 1 0 0
P7 0 12 2 2 5 7 0 0 1 0
P8 0 23 9 -5 -3 8 0 0 0 1
Z 0 -4 -7 -3 -2 0 0 0 0

3. INVESTIGACIÓN OPERATIVA I
ABIAIL CRIOLLO
5TO SEMESTRE “A”
3
Tabla 2 4 7 3 2 0 0 0 0
Base Cb P0 P1 P2 P3 P4 P5 P6 P7 P8
P5 0 4 -0.2 0 -4.4 0.8 1 -0.8 0 0
P2 7 2 0.8 1 1.6 1.8 0 0.2 0 0
P7 0 8 0.4 0 1.8 3.4 0 -0.4 1 0
P8 0 33 13 0 5 17 0 1 0 1
Z 14 1.6 0 8.2 10.6 0 1.4 0 0
La solución óptima es Z = 14
X1 = 0
X2 = 2
X3 = 0
X4 = 0