Ejercicios PL Mtodo Grfico

1. Maximizar Z = 3X1 + 5X2 s.a.: 3X1 + 2X2 18 X1 4 X2 6 X1, X2 0

8. Maximizar Z = 50X1 + 40X2 s.a.: 3X1 + 5X2 150 X2 20 8X1 + 5X2 300 X1, X2 0

2 Maximizar Z = 2X1 + 3X2 s.a.: X1 + 2X2 40 2 X1 - X2 8 - X1 + 5 X2 5 X1, X2 0

9. Maximizar Z = 10X1 + 9X2 s.a.: 7/10X1 + X2 630 1/2X1 + 5/6X2 600 X1 + 2/3X2 708 1/10X1 + 1/4X2 135 X1, X2 0

3. Maximizar Z = 10X1 + 20X2 s.a.: 0.05X1 + 0.05X2 1 100 0.05X1 + 0.10X2 1 800 0.10X1 + 0.05X2 2 000 X1, X2 0

10. Maximizar Z = 10X1 + 9X2 s.a.: 7/10X1 + X2 630 1/2X1 + 5/6X2 600 X1 + 2/3X2 708 1/10X1 + 1/4X2 135 X1, X2 0

4 Maximizar Z = 5X1 + 4X2 s.a.: 6X1 + 4X2 24 X1 + 2X2 6 X2 2 X1, X2 0

11. Maximizar Z = X1 + X2 s.a.: X1 + 5X2 5 1/2X1 + 5/6X2 600 2X1 + X2 4 X1, X2 0

5. Maximizar Z = 2X1 + 3X2 s.a.: X1 + X2 6 X1 3 X2 2 X1, X2 0

12. Maximizar Z = 3X1 + 4X2 s.a.: 7/10X1 + X2 630 2X1 + X2 6 2X1 + 3X2 9 X1, X2 0

6 Maximizar Z = X1 + X2 s.a.: X1 + 2X2 6 6X1 + 4X2 24 X1, X2 0

13. Maximizar Z = 10X1 + 14X2 s.a.: 4X1 + 6X2 24 2X1 + 6X2 20 X1, X2 0

7 Maximizar Z = 7X1 + 10X2 s.a.: 7X1 + 7X2 49 10X1 + 5X2 50 X1, X2 0

14. Maximizar Z = 1X1 + 1.5X2 s.a.: 0.5X1 + X2 20 0.5X1 - 0.5X2 4 - 0.5X1 + 2.5 X2 2.5 X1, X2 0

Ejercicios Casos Especiales

Maximizar Z = 5X1 + 10X2

s.a.: 3X1 + 9X2 9 2X1 + 3X2 12 4X1 - 3X2 8 X1, X2 0

No Factible

Maximizar Z = 7X1 + 4X2

s.a.: -2X1 + 3X2 6 X1 + X2 2 5X1 - 4X2 10 X1, X2 0

Degenerado

X2 =0 S1=10

X1=2 Z=14

Maximizar Z = 2X1 + X2

s.a.: X1 - X2 1 -X1 + X2 1 X1, X2 0

No Acotado

Maximizar Z = 6X1 + 7X2+ 6X3

s.a.: 2X1 + X2 + 2X3 20 X1 + 2X2 + 3X3 20 2X1 + 2X2 + X3 20 X1, X2, X3 0

Degenerado

Maximizar Z = 7X1 + 4X2 s.a.: 3X1 - 2X2 = 6

-3X1 + 9X2 9 X1 1 X1, X2 0

No Factible A=3

S1=12

X1=1 Z=77

Maximizar Z = 4X1 + 4X2 s.a.: -2X1 + 2X2 2 -X1 + 2X2 4 X1, X2 0

No Acotado

6. Maximizar Z = 10X1 + 5X2 ptimos alternos s.a.: 4X1 + 2X2 16 3X1 + 3X2 18 X2 3

X1, X2 0