Ejercicios De I O

1. OMAR SANCHEZ GUEVARA
EJERCICIOS UNIDAD #3
1. PROBLEMA 1
MAX Z = 10X1 + X2
Sa 2X1 + 5X2 ≤ 11
X1, X2 ≥ 0 y enteras
SUBPROBLEMA 1
MAX Z = 10X1 + X2
Sa 2X1 + 5X2 ≤ 11
X1, X2 ≥ 0 y enteras
(X1 = 5.5; X2 = 0)
FO: Z = 55
SUBPROBLEMA 2 =
MAX Z = 10X1 + X2
Sa 2X1 + 5X2 ≤ 11
X1 ≤ 5
X1, X2 ≥ 0 y enteras
(X1 = 5; X2 = 0.2)
FO: Z = 50.2
SUBPROBLEMA 3
MAX Z = 10X1 + X2
Sa 2X1 + 5X2 ≤ 11
X1 ≥ 6
X1, X2 ≥ 0 y enteras
NO TIENE SOLUCION

2. SUBPROBLEMA 4
MAX Z = 10X1 + X2
Sa 2X1 + 5X2 ≤ 11
X1 ≤ 5
X2 ≤ 0
X1, X2 ≥ 0 y enteras
(X1 = 5; X2 = 0)
FO: Z = 31
SUBPROBLEMA 5
MAX Z = 10X1 + X2
Sa 2X1 + 5X2 ≤ 11
X1 ≤ 5
X2 ≥ 1
X1, X2 ≥ 0 y enteras
(X1 = 3; X2 = 1)
FO: Z = 31

3. SUBPROBLEMA 1
Z = 55
X1 = 5.5
X2 = 0
SUBPROBLEMA 2
Z = 50.2
X1 = 5
X2 = 0.2
SUBPROBLEMA 3
IMPOSIBLE
SUBPROBLEMA 4
Z = 50
X1 = 5
X2 = 0
SUBPROBLEMA 5
Z = 31
X1 = 3
X2 = 1
X1 ≤ 5
X2 ≤ 0
X1 ≥ 6
X2 ≥ 1

4. 2. PROBLEMA 2
MAX Z = 3X1 + 4X2
Sa 2X1 + 3X2 ≤ 9
X1, X2 ≥ 0 y enteras
SUBPROBLEMA 1
MAX Z = 3X1 + 4X2
Sa 2X1 + 3X2 ≤ 9
X1, X2 ≥ 0 y enteras
(X1 = 4.5; X2 = 0)
FO: Z = 13.5
SUBPROBLEMA 2
MAX Z = 3X1 + 4X2
Sa 2X1 + 3X2 ≤ 9
X1 ≤ 4
X1, X2 ≥ 0 y enteras
(X1 = 4; X2 = 0.333)
FO: Z = 13.333
SUBPROBLEMA 3
MAX Z = 3X1 + 4X2
Sa 2X1 + 3X2 ≤ 9
X1 ≥ 5
X1, X2 ≥ 0 y enteras
NO TIENE SOLUCION

5. SUBPROBLEMA 4
MAX Z = 3X1 + 4X2
Sa 2X1 + 3X2 ≤ 9
X1 ≤ 4
X2 ≤ 0
X1, X2 ≥ 0 y enteras
(X1 = 4; X2 = 0)
FO: Z = 12
SUBPROBLEMA 5
MAX Z = 3X1 + 4X2
Sa 2X1 + 3X2 ≤ 9
X1 ≤ 4
X2 ≥ 1
X1, X2 ≥ 0 y enteras
(X1 = 3; X2 = 1)
FO: Z = 13

6. SUBPROBLEMA 1
Z = 13.5
X1 = 4.5
X2 = 0
SUBPROBLEMA 2
Z = 13.333
X1 = 4
X2 = 0.333
SUBPROBLEMA 3
IMPOSIBLE
SUBPROBLEMA 4
Z = 12
X1 = 4
X2 = 0
SUBPROBLEMA 5
Z = 13
X1 = 3
X2 = 1
X1 ≤ 4
X2 ≤ 0
X1 ≥ 5
X2 ≥ 1

7. 3. PROBLEMA 3
MAX Z =11X1 + 9X2
Sa X1 + X2 ≤ 1
3X1 + X2 ≤ 2
X1, X2 ≥ 0 y enteras
SUBPROBLEMA 1
MAX Z =11X1 + 9X2
Sa X1 + X2 ≤ 1
3X1 + X2 ≤ 2
X1, X2 ≥ 0 y enteras
(X1 = 0.5; X2 = 0.5)
FO: Z = 10
SUBPROBLEMA 2
MAX Z =11X1 + 9X2
Sa X1 + X2 ≤ 1
3X1 + X2 ≤ 2
X1 ≤ 0
X1, X2 ≥ 0 y enteras
(X1 = 0; X2 = 1)
FO: Z = 9

8. SUBPROBLEMA 2
MAX Z =11X1 + 9X2
Sa X1 + X2 ≤ 1
3X1 + X2 ≤ 2
X1 ≥ 1
X1, X2 ≥ 0 y enteras
NO TIENE SOLUCION
SUBPROBLEMA 1
Z = 13.5
X1 = 4.5
X2 = 0
SUBPROBLEMA 2
Z = 9
X1 = 0
X2 = 1
SUBPROBLEMA 3
IMPOSIBLE
X1 ≤ 0 X1 ≥ 1