Варіанти задач

1.	2.
3.	4.
5.	6.
7.	8.
9.	10.
11.	12.
13.	14.
15.	16.
17.	18.
19.	20.
21.	22.
23.	24.
25.	26.
27.	28.
29.	30.

4.6. Лабораторна робота 6

Розв’язання задачі лінійного програмування за допомогою модифікованого симплекс-методу

Мета – навчитися використовувати модифікований симплекс-метод та знаходити оптимальний план задачі цілочислового лінійного програмування за критерієм оптимальності

Варіанти задач

1. F = 4x1 + 2 x2 + x3 Þ max x1 + x2 ≥ 10 2x1 + x2 + x3 ≤ 4 x1, x2 ,x3 ≥ 0.	2. F = 2 x1 + 3 x2 Þ min 2 x1 - x2 + x3 ≥ 3 x1 - x2 + x3 ≤ 2 x1,x2 ≥ 0.
3. F = x1 + 3 x2 + x3 Þ max 3 x1 + 2 x2 - x3 ≤ 5 - x1 + 4 x2 + 2 x3 ≤ 3 2 x1 - 5 x2 + x3 ≤ 2 x1, x2 ,x3 ≥ 0.	4. F = 2 x1 + x2 + 4 x3 - x4 Þ max 4 x1 - x2 + 3 x3 + x4 ≤ 17 x1 + 2 x2 - 2 x3 - x4 = 1 - 3 x1 + x2 + 5 x3 ≥ 2 x1,…,x4 ≥ 0.
5. F = 4 x1 + 3 x2 + x3 Þ min 3 x1 - x2 + 2x3 ≥ 1 2 x1 + 4x2 - 5x3 ≤ 3 - x1 + 2x2 + x3 ≤ 8 x1, x2 ,x3 ≥ 0.	6. F = 2 x1 - x2 + 4 x3 + x4 Þ max x1 + 2 x2 + 3 x3 + x4 ≤ 7 - 3 x1 + 4 x2 - x3 + 4 x 4 ≤ 15 2 x1 - 5 x2 + 2 x3 + 2 x4 ≤ 2 x1,…,x4 ≥ 0.
7. F = 3 x1 + 4 x2 + 3 x3 + x4 Þ max 2 x1 + 4 x2 + x4 ≤ 12 7 x1 + 2 x2 + 2 x3 + 6 x4 ≤ 8 5 x1 + 8 x2 + 4 x3 + 3 x4 ≤ 48 x1,…,x4 ≥ 0.	8. F = 6 x1 + 4 x2 + 12 x3 + 10 x4 Þ min 2 x1 + 3 x2 +4 x3 + x4 ≥ 3 2 x1 + x2 + 4 x3 - 2 x 4 ≤ 4 x2 + 2 x3 + 3 x4 ≥ 6 x1,…,x4 ≥ 0.
9. F = 7 x1 + 15 x2 + 2 x3 + 30 x4 Þ min x1 - 3 x2 + 2 x3 - 3 х4 ≥ 2 - 2 x1 - 4 x2 + 5 x3 + 2 x4 ≤ 1 3 x1 - x2 + 2 x3 - x4 ≥ 4 x1 + 3 x2 + 2 x3 - 4 x4 ≥ 4 x1 ,…, x4 ≥ 0.	10. F = 2 x1 - x2 + x3 Þ max x1 + x2 + x3 ≥ 6 2 x1 - x2 + x3 ≤ 2 x1, x2 ,x3 ≥ 0.
11. F = 12 x1 + 27 x2 + 6 x3 Þ min 2x1 + 3 x2 + 2 x3 ≤ 14 x1 + 3 x2 + x3 ≥ 6 6x1 + 9 x2 + 2 x3 ≤ 22 x1, x2 ,x3 ≥ 0.	12. F = 3 x1 + 5 x2 +4 x3 Þ min 3 x1 + 4 x2 + 2x3 ≤ 9 2 x1 + 5 x2 + x3 ≤ 8 x1 + 2 x2 + 4x3 ≥ 7 x1,x2 , x3≥ 0.
13. F = 3 x1 - x2 + x3 Þ max 2 x1 + 3 x2 - 2x3 ≥ 18 2 x1 + x2 + x3 ≤ 12 3 x1 + 2 x2 + 2x3 ≤ 18 x1, x2 ,x3 ≥ 0.	14. F = 2 x1 + x2 + 4 x3 - x4 Þ max 24 x1 + x2 + 2 x3 ≥ 17 x1 + x2 - x3 ≤ 5 4 x1 + x2 - 2 x3 ≤ 7 x1, x2 ,x3 ≥ 0.
15. F = 2 x1 + x2 + x3 Þ max x2 + x3 ≤ 9 x1 + x2 +2 x3 ≥ 9 x1 + x2 + x3 ≤ 10 x1, x2 , x3 ≥ 0.	16. F = x1 + 3 x2 + x3 Þ max x1 + 2 x2 - x3 ≥ 6 4 x1 - x2 + x3 ≤ 12 x1 + 3 x2 - 2 x3 ≤ 6 x1, x2 ,x3 ≥ 0.
17. F = 2 x1 - 3 x4 + x5 +2 x6 Þ min x1 + x2 - 3x4 + 2 x6 ≤ 5 2 x2 - 3 x3 + x 4 + x5 ≤ 4 3x1 - x2 + 2 x3 + 3 x5 ≥ 3 x1,…,x6 ≥ 0.	18. F = 5x1 + 2 x2 - 3 x3 + x4 Þ min 2 x1 - x2 + x3 + x4 = 5 x1 + x2 - x3 + x 4 ≤ 2 5 x1 - 8x2 + 2 x3 + 4 x4 ≥3 x1,…,x4 ≥ 0.
19. F = 2 x1 + 3 x2 Þ max 2 x1 - x2 ≥ 5 - x1 + 3 x2 ≤ 3 x1 + x2 = 4 x1 - 2 x2 ≥ 8 x1 , x2 ≥ 0.	20. F = x1 + x2 + x3 Þ max 3 x1 + 2 x2 + x3 ≤ 3 4 x1 + 5 x2 + 2 x3 ≥ 1 2 x1 + x2 + 4 x3 = 6 x1, x2 ,x3 ≥ 0.
21. F = 5x1 + 2 x2 - 3 x3 + x4 Þ max - x1 + x2 + 3 x3 - x4 ≤ 2 x1 + x2 + x3 + 3 x 4 ≥ 3 x1,…,x4 ≥ 0.	22. F = - x1 + 4 x2 Þ max x1 - 3 x2 ≥ 3 x1 + x2 ≤ 10 3x1 + x2 ≥ 9 -x1 + x2 ≤ 4 x1 , x2 ≥ 0.
23. F = 5x1 + 5x2 - 9 x3 Þ max 3 x1 - x2 - x3 - 5 x4 ≤ 1 x1 + 4 x2 + 4 x3 + 2x4 ≤ 1 x1 , …, x4 ≥ 0.	24. F = 6x1 + 5x2 Þ max 2 x1 + 3 x2 ≤ 12 3 x1 + 2 x2 ≤ 10 2 x1 + x2 ≤ 18 x1 , x2 ≥ 0.
25. F = 3x1 + 5x2 Þ max 2 x1 - 3 x2 ≤ 6 - 2 x1 + x2 ≤ 4 x1 + x2 ≤ 20 x1 , x2 ≥ 0.	26. F = -2x1 + x2 - 3x3 Þ min 3 x1 - x3 ≤ 8 - x1 + x2 + 4 x3 ≤ 1 2 x1 + x2 - 3 x3 ≤ 6 x1, x2 , x3 ≥ 0.
17. F = 10x1 - 7x2 - 5x3 Þ min 6 x1 + 15 x2 + 6x3 ≤ 9 14 x1 + 42 x2 + 16x3 ≤ 21 2 x1 + 8x2 + 2 x3 ≤4 x1, x2 , x3 ≥ 0.	18. F = x1 -3x2 + x3 Þ min 3 x1 - x2 + 2 x3 ≤ 7 - 2 x1 + 4 x2 ≤ 12 - 4 x1 + 3 x2 + 3 x3 ≤ 10 x1, x2 , x3 ≥ 0..
19. F = 3x1 - x2 Þ max 4 x1 - x2 ≥ 20 - 3 x1 + 2x2 ≤ 15 3 x1 + x2 ≥ 30 x1 - 2x2 ≤ 20 x1 , x2 ≥ 0	20. F = 2 x1 + 4 x2 + x3 + x4 Þ max x1 + 3x2 + x4 ≤ 4 2 x1 + x2 ≤ 3 x2 + 4x3 + x4 ≤ 3 x1,…,x4 ≥ 0.
21. F = - x1 + 2x2 Þ min x1 + 3x2 ≥ 6 - x1 + 2x2 ≤ 1 x1 + x2 ≤ 5 3x1 - x2 ≥ 6 x1 , x2 ≥ 0	22. F = 3 x1 - x2 Þ max -3 x1 + 2x2 ≤ 15 4 x1 - x2 ≥ 20 x1 - 2 x2 ≤ 20 3x1 + x2 ≥ 30 x1 , x2 ≥ 0
23. F = 3x1 + 5x2 + 4x3 Þ max 3 x1 + 4 x2 + 2x3 ≤ 9 2 x1 + 5 x2 + x3 ≤ 8 x1 + 2x2 + 4 x3 ≥ 7 x1, x2 , x3 ≥ 0.	24. F = x1 + 2x2 Þ max 2 x1 + x2 ≤ 18 x1 + 2x2 ≥ 14 x1 -+ 2x2 ≤ -10 x1 , x2 ≥ 0
25. F = x1 + 2x2 Þ max x1 + x2 ≤ 4 x1 + 5x2 ≥ 3 x1 , x2 ≥ 0	26. F = - 5x1 - 6x2 Þ min -x1 + 2x2 ≥ -6 x1 + 2x2 ≤ 12 x1 + x2 ≤ 8 x1 , x2 ≥ 0
27. F = x1 + 2x2 Þ max x1 + 5x2 ≥ 3 x1 + x2 ≤ 4 x1 ≤ 3 x1 , x2 ≥ 0	28. F = 2x1 - 3x2 + 4x3 Þ max 2x1 + 3x2 - 4x3 ≤ 15 x1 + x2 + 3 x3 ≤ 12 3x1 - 3x2 + 5 x3 ≥ 17 x1, x2 , x3 ≥ 0.
29. F = 4x1 - x2 + 5x3 Þ max 2 x1 - 5 x2 + 7x3 ≤ 13 2 x1 + 3 x2 - 4x3 =16 4 x1 + 3x2 - 7x3 ≤ 10 x1, x2 , x3 ≥ 0.	30. F = 2x1 + 2x2 - 3x3 Þ max x1 + x2 - x3 ≥ 12 2 x1 - 3 x3 ≤ 10 3 x1 - 2x2 + x3 ≥ 16 x1, x2 , x3 ≥ 0.