Записати наступні задачі лінійного програмування у канонічній формі
ЗАВДАННЯ ДЛЯ САМОСТІЙНОГО ВИКОНАННЯ
Всі змінні задачі повинні бути невід’ємні.
А в ліву частину нерівностей
ai1x1 + ai2x2 + … + ainxn ≥ bi
xn+1 вводиться зі знаком “-”: ai1x1 + ai2x2 + … + ainxn - xn+1 = bi, xn+1 ≥ 0.
Приведемо обмеження задачі до вигляду рівностей. В ліві частини першої та другої нерівностей виду “≥” введемо відповідно додаткові невід’ємні змінні х4 та х5 зі знаком “-”, а в ліву частину третьої нерівності виду “≤” введемо додаткову невід’ємну змінну х6 зі знаком “+”.
4х1 - х2 - х4 = -5,
2х2 + 3х3 - х5 = 15,
х1 - 2х3 + х6 = 7.
Якщо серед змінних є такі, на знак яких обмежень не накладено, то перехід від цих змінних до невід’ємних здійснюється за допомогою заміни кожної такої змінної xj різницею двох нових невід’ємних змінних xj’ i xj’’: xj = xj’ - xj’’, де xj’ ≥ 0, xj’’ ≥ 0.
В умові нашої задачі х1 , х2 ≥ 0, а х4 , х5 , х6 ≥ 0, згідно пункту 2. Так як на знак змінної х3 обмежень не накладено, то замінюємо її різницею двох нових невід’ємних змінних x3’ i x3’’: x3 = x3’ - x3’’, де x3’ ≥ 0, x3’’ ≥ 0 і робимо відповідну заміну в цільовій функції і в усіх обмеженнях задачі. Отже, остаточно маємо таку канонічну форму задачі лінійного програмування:
L = -2 х1 - 3х2 + x3’ - x3’’ - 2 → mах
4х1 - х2 - х4 = -5,
2х2 + 3 x3’ - 3x3’’ - х5 = 15,
х1 - 2 x3’ + 2x3’’ + х6 = 7,
х1 , х2 , x3’ , x3’’ ,х4 , х5 , х6 ≥ 0.
| 1. L = -x1 - 2x2 + х3 → min, 2x1 - 3x2 + 4х3 ≤ 11, x1 - 5x2 + 10 х3 = 13, -3x1 + 5x2 + 3 х3 ≤ 17, x1, x2, x3 ≥ 0. | 2. L = -x1 - 3x2 + 5х3 → max, 4x1 + x2 + 3х3 ≤ 11, 6x1 - 2x2 + 8 х3 = 15, 2x1 - 3x2 - 2х3 ≥ 16, x1, x2, x3 ≥ 0. | 3. L = 2x1 - 4x2 – 8х3 → min, x1 - x2 - х3 ≥ 6, 2x1 - x2 + х3 ≤ 12, x1 + x2 + 2х3 ≥ 20, x1, x2, x3 ≥ 0. |
| 4. L = -5x1 - 8x2 - х3 → min, 5x1 + 2x2 - 7х3 ≤ 12, -4x1 + 6x2 + 8х3 ≥ 15, x1 - 2x2 + 10х3 ≤ 11, x1, x2, x3 ≥ 0. | 5. L = 3x1 + 2x2 - 3х4 – x5 → max, 2x1 + x3 - 2х4 + 3x5 ≤ 7, x1 - x3 + 2х4 + 2x5 ≤ 2, 2x2 + 2x3 - 3 х4 + 2x5 ≤ 8, x1 + 4x4 - 2х5 ≥ 9, x1, x2, x3, x4, x5 ≥ 0. | 6. L = -x1 + 3x2 - 2х3 + 2x4 → min, x1 - 2x2 – х3 + x4 ≤ 3, x1 + x2 + 2х3 - 2x4 ≥ 7, 3x1 - x2 + х3 + 2x4 ≤ 9, -x1 + 3x2 + 4x3 + 3х4 = 12, x1, x2, x3, x4 ≥ 0. |
| 7. L = 5,6x1 + 5,7x3 + 5,2х4 - 5x5 → max, x1 + 2x3 + x4 = 12, 2x1 – x3 + 2х4 – x5 = 14, x1 + x3 + 10x4 ≤ 20, x1, x2, x3, x4, x5 ≥ 0. | 8. L = -2x1 - 3x2 + х3 → max, 6x1 + 4x2 + 2х3 ≤ 22, -2x1 + x2 + 3х3 ≥ 13, 3x1 - 9x2 + 3х3 = 3, x1, x2, x3 ≥ 0. | 9. L = 2x1 + 3x2 → max, x1 + 2x2 ≤ 9, -2x1 + 3x2 ≤ 7, 2x1 + x2 ≥ 8, x1, x2 ≥ 0. |
| 10. L = -2x1 + 3x2 - 6х3 – x4 → min, 2x1 + x2 - 2х3 + x4 = 24, x1 + 2x2 + 4х3 ≤ 22, -2x1 + x2 + 3х3 ≥ 13, 3x1 - 9x2 + 3x3 = 3, x1, x2, x3, x4 ≥ 0. | 11. L = -2x1 - 3x2 + х3 → max, 6x1 + 4x2 + 2х3 ≥ 10, 2x1 - х3 ≤ 15, 7x1 + x2 - х3 ≥ 12, x1, x2, x3 ≥ 0. | 12. L = 10x1 + 2x2 + 12х3 → max, x1 + 2x2 + 3х3 ≤ 120, x1 + 7x2 + 6х3 ≤ 220, 6x1 + 4x2 + 5х3 ≤ 210, 4x1 - 6x2 + 6x3 ≤ 350, x1, x2, x3 ≥ 0. |
| 13. L = 3x1 + 4x2 → max, 12x1 + x2 ≤ 30, 4x1 + 3x2 ≤ 12, 12x1 + 3x2 ≤ 25, x1, x2 ≥ 0. | 14. L = 3x1 + 2x2 + 4х3 → min, 6x1 + 2x2 - 2х3 ≤ 8, x1 + 2x2 + 4х3 ≥ 8, x1 - x2 + 2х3 = 6, x1, x2, x3 ≥ 0. | 15. L = 3x1 + 3x2 + 2х3 → max, x1 - x2 + 2х3 ≤ 4, -2x1 + x2 + х3 ≥ 2, 4x1 + 2x2 = 4, x1, x2, x3 ≥ 0. |
| 16. L = 2x1 + x2 - х3 → min, 3x1 - x2 + х3 ≤ 5, 2x1 - x2 - х3 ≥ 6, x1, x2, x3 ≥ 0. | 17. L = 2x1 + 3x2 - х3 → max, 2x1 - x2 + х3 ≤ 8, 4x1 + 2x2 - х3 = 5, x1, x2, x3 ≥ 0. | 18. L = -3x1 + 2x2 + х3 → max, -x1 + 2x2 + х3 = 4, 3x1 + 2х3 ≥ 12, x1, x2, x3 ≥ 0. |
| 19. L = 2x1 + x2 + х3 → max, x1 - x2 + х3 ≥ 1, x2 + х3 ≤ 1, x1 + x2 + х3 = 3, x1, x2, x3 ≥ 0. | 20. L = -x1 - x2 - х3 + x4 – x5 + x6 → max, x1 + 2x2 + 2х4 + x5 = 6, 6x2 + x5 + х6 = 9, 4x2 – x3 + 2х4 + 6x6 = 4, x1, x2, x3 , x4, x5, x6 ≥ 0. | 21. L = 9x1 + x2 – x3 → min, x1 - 5x2 ≤ 5, -x1 + 4x3 ≤ 4, x1 + x2 ≤ 8, x1, x2 ≥ 0. |
| 22. L = 4x1 + 3x2 + x3→ min, x1 + x2 ≤ 6, 3x1 + 10x2 ≤ 26, x1 + 11x3 ≤ 20, x1, x2 ≥ 0. | 23. L = -2x1 + 3x2 - 5x3 → min, 2x1 + x3 ≤ 8, -2x2 + 3x3 ≤ 6, 2x1 + 4x2 ≥ 8, x1, x2 ≥ 0. | 24. L = x1 + 3x2 + x5 → min, 2x1 – x3 ≥ 4, x1 - x2 ≥ 1, 2x1 + x3 ≤ 6, x1, x2 ≥ 0. |
| 25. L = -2x1 + 5x2 – 2x3→ min, x1 + x2 + x3 ≥ 3, x1 ≥ 2, x2 ≤ 8, x1, x2 ≥ 0. | 26. L = 2x1 + x2 – 2x3→ min, x1 – x3 ≥ -3, 6x2 + 7x3 = 42, 2x1 - 3x2 ≤ 6, x1, x2 ≥ 0. | 27. L = 2x1 + 5x2 + x5 → min, -2x1 + 3x3 ≤ 1, x2 - x3 ≤ 1, x1 + 2x2 ≤ 2, x1, x2 ≥ 0. |
| 28. L = x1 + 3x2 – x3→ min, 5x1 - 2x2 ≥ 7, -x2 + x3 = 5, x1 + x3 ≤ 6, x1, x2 ≥ 0. | 29. L = -2x1 + 4x2 – 5x3→ min, 2x1 + x2 ≤ 8, x2 + 3x3 ≥ 6, 3x1 + x3 = 3, x1, x2 ≥ 0. | 30. L = 2x1 - 4x2 + x3→ min, 8x1 - 5x2 = 16, x2 + 3x3 ≥ 2, 2x1 + 7x3 ≤ 9, x1, x2 ≥ 0. |
| 31. L = -2x1 + x2 – x3→ min, 2x1 + x2 = 8, x2 + x3 ≤ 6, -3x1 + 2x3 ≥ 3, x1, x2 ≥ 0. | 32. L = x1 + 3x2 + x3→ min, 2x1 - 3x2 = 12, -x1 + 2x3 = 8, 3x2 + 2x3 ≤ 24, x1, x2 ≥ 0. | 33. L = 7x1 + 5x2 + 3x3→ min, 7x1 + 5x3 ≥ 7, 7x2 – 5x3 = 35, x1 - x2 ≤ 0, x1, x2 ≥ 0. |
| 34. L = 3x1 + x2 – x3→ max, 3x1 + 5x2 ≥ 15, 5x2 + 3x3 ≤ 15, 2x1 + 3x3 ≥ 1, x1, x2 ≥ 0. | 35. L = x1 + 3x2 + 2x3→ max, 6x1 + 7x2 ≤ 89, 3x2 + 5x3 ≥ 16, 5x1 + 3x3 ≥ 1, x1, x2 ≥ 0. | 36. L = -4x1 - 3x2 + 15x3→ max, 6x1 + 3x2 ≤ 18, -4x2 + x3 ≥ 5, 3x1 – x3 ≤ 7, x1, x2 ≥ 0. |
| 37. L = x1 + 2x2 - 3х3 – x4 → min, 3x1 + x2 - 2х3 + 4x4 = 21, 3x1 - 2x2 + х3 ≤ 13, -2x1 + x2 + 3х3 ≥ 17, x1 - 8x2 + 7x3 = 8, x1, x2, x3, x4 ≥ 0. | 38. L = -2x1 + 3x2 - 4х3 + 5x4 → min, -x1 + x2 - х3 + x4 = 18, x1 - 2x2 + х3 - 2x4 ≤ 13, x1 + x2 + 3х3 + 9x4 ≥ 14, x1 - 3x2 + 2x3 = 3, x1, x2, x3, x4 ≥ 0. | 39. L = -3x1 + 2x2 - х3 + 4x4 → min, x1 + 3x2 - 2х3 + 4x4 ≥ 12, x1 + 2x3 + 3х4 ≤ 23, 2x2 + 3x3 + 4х4 ≥ 12, 2x1 - 9x2 + 5x3 = 4, x1, x2, x3, x4 ≥ 0. |
| 40. L = -4x1 - 3x2 + 2x3→ max, 2x1 + 5x3 ≤ 10, 7x2 + 3x3 ≤ 21, 2x1 + x2 ≥ 2, x1, x2 ≥ 0. | 41. L = -x1 - 3x2 + 5х3 → min, 4x1 + x2 + 3х3 ≥ 11, 6x1 - 2x2 + 8 х3 ≤ 15, 2x1 - 3x2 - 2х3 ≤ 16, x1, x2, x3 ≥ 0. | 42. L = 2x1 + 5x2 + 19x3→ max, 3x2 + 7x3 ≥ 24, 2x1 – x3 ≤ 3, -x1 + 2x2 ≤ 4, x1, x2 ≥ 0. |
| 43. L = x1 + 2x2 + 3х3 + 4x4 → min, 3x1 + 7x2 + 8х3 + 9x4 ≥ 21, x1 - x2 + х3 - x4 ≤ 23, x1 + x2 - х3 + x4 ≥ 27, x1 - 8x2 + 7x3 + 2x4 ≤ 39, x1, x2, x3, x4 ≥ 0. | 44. L = -17x1 + 19x2 + 23х3 - 29x4 → min, 3x1 + 7x2 - 11х3 + 13x4 ≥ 24, x1 - 5x2 + 9х3 - 21x4 ≤ 29, x1 + 12x2 + 13х3 + x4 ≥ 34, 11x1 - 9x2 + 3x3 + 2x4 ≤ 35, x1, x2, x3, x4 ≥ 0. | 45. L = 19x1 - 13x2 + 15х3 - 18x4 → min, 6x1 + x2 + 4х3 + 12x4 ≥ 38, 4x1 + 3x2 + 8х3 + 11x4 ≥ 45, x1 + x2 + х3 + x4 ≤ 49, x1 - 2x2 + 3x3 + 4x4 ≤ 16, x1, x2, x3, x4 ≥ 0. |
| 46. L = 9x1 + 4x2 + 3х3 + 7x4 → max, 3x1 + 7x2 + 8х3 + 9x4 ≥ 21, x1 - x2 + х3 - x4 ≤ 23, x1 + x2 - х3 + x4 ≥ 27, x1 - 8x2 + 7x3 + 2x4 ≤ 39, x1, x2, x3, x4 ≥ 0. | 47. L = 7x1 + 3x2 -5х3 → min, 3x1 + x3 ≤ 4, 3x2 + 2x3 ≤ 5, x1 + x2 ≥ 1, x1 ≤ 3, x2 ≤ 1, x1, x2, х3 ≥ 0. | 48. L = 6x1 - 15x2 + 4х3 - 2x4 → max, 11x1 + 8x2 + х3 - 6x4 ≥ 2, 9x1 - 6x2 + х3 – 2x4 ≤ 3, x1 + x2 - х3 + x4 ≤ 1, x1 - 2x2 + 5x3 + x4 ≤ 12, x1, x2, x3, x4 ≥ 0. |
| 49. L = -x1 - 2x2 + х3 → max, 2x1 - 3x2 + 4х3 ≥ 11, x1 - 5x2 + 10 х3 ≤ 13, -3x1 + 5x2 + 3 х3 ≤ 17, x1, x2, x3 ≥ 0. | 50. L = 2x1 - 4x2 – 8х3 → min, x1 - x2 - х3 ≥ 6, 2x1 - 3x2 + 4х3 ≤ 12, x1 + x2 + 2х3 ≥ 10, x1, x2, x3 ≥ 0. | 51. L = 7x1 - 8x2 - х3 → min, -3x1 + 2x2 - 7х3 ≤ 12, 2x1 + 6x2 + 8х3 ≥ 15, x1 - 2x2 + 10х3 ≤ 13, x1, x2, x3 ≥ 0. |
| 52. L = 5x1 + 2x2 + 3х3 → min, 2x1 + x2 ≤ 3, 5x2 + 3x3 ≤ 8, x1 + 3x3 ≥ 3, x2 ≤ 5, x3 ≤ 2, x1, x2, х3 ≥ 0. | 53. L = 6x1 + 5x2 +3х3 → min, 3x1 + 2x3 ≤ 5, x2 + x3 ≤ 2, x1 + 2x2 ≥ 2, x1 ≤ 1, x3 ≤ 2, x1, x2, х3 ≥ 0. | 54. L = 4x1 - 3x2 - х3 → min, 2x1 + 7x3 ≤ 3, x2 + x3 ≤ 2, 3x1 + 2x2 ≥ 6, x1 ≤ 11, x2 ≤ 12, x1, x2, х3 ≥ 0. |
| 55. L = 5x1 + 3x2 - х3 → min, 5x1 + 2x3 ≤ 7, 5x2 + 4x3 ≤ 5, 3x1 + 2x2 ≥ 3, x2 ≤ 5, x3 ≤ 2, x1, x2, х3 ≥ 0. | 56. L = 7x1 + 5x2 + х3 → min, 6x1 + 5x2 ≤ 11, x1 + x3 ≤ 2, 2x2 + x3 ≥ 2, x1 ≤ 11, x2 ≤ 5, x1, x2 ≥ 0. | 57. L = x1 + x2 + х3 → min, 3x1 + 5x2 ≤ 8, 5x1 + 3x3 ≤ 6, x2 + 3x3 ≥ 3, x2 ≤ 3, x3 ≤ 3, x1, x2, х3 ≥ 0. |
| 58. L = 7x1 + 4x2 - 5х3 → min, 2x1 + x2 ≤ 3, 7x2 + 5x3 ≤ 12, x1 + 2x3 ≥ 4, x2 ≤ 7, x3 ≤ 11, x1, x2 ≥ 0. | 59. L = 2x1 + x2 + 3х3 → max, 3x1 + x2 ≤ 4, 2x2 + 3x3 ≤ 5, x1 + x3 ≥ 2, x1 ≤ 1, x2 ≤ 2, x1, x2 ≥ 0. | 60. L = 3x1 + x2 - 7х3 → max, 4x1 + x2 ≤ 5, 3x2 + 2x3 ≤ 5, 3x1 + x3 ≥ 6, x2 ≤ 13, x3 ≤ 11, x1, x2 ≥ 0. |
| 61. L = x1 - 2x2 – 4х3 → max, x1 - x2 - х3 ≥ 3, 2x1 - 3x2 + 4х3 ≤ 6, x1 + x2 + 2х3 ≥ 5, x1, x2 ≥ 0. | 62. L = 9x1 + 10x2 - 3х3 → max, 4x1 + x2 - 2х3 ≥ 5, x1 ≥ 4, x2 ≤ 2, x3 ≥ 3, x1, x2 ≥ 0. | 63. L = 7x1 - 8x2 - х3 → max, -3x1 + 2x2 - 7х3 ≤ 6, 2x1 + 6x2 + 8х3 ≥ 5, x1 - 2x2 + 9х3 ≤ 3, x1, x2 ≥ 0. |
| 64. L = 5x1 + 2x2 + 3х3 → max, 2x1 + x2 ≤ 3, 5x2 + 3x3 ≤ 8, x1 + 3x3 ≥ 3, x2 ≥ 7, x3 ≥ 9, x1, x2 ≥ 0. | 65. L = 7x1 + 3x2 -5х3 → max, 3x1 + x3 ≤ 4, 3x2 + 2x3 ≤ 5, x1 + x2 ≥ 1, x1 ≥ 3, x2 ≥ 1, x1, x2 ≥ 0. | 66. L = 4x1 - 3x2 - х3 → max, 2x1 + 7x3 ≤ 3, x2 + x3 ≤ 2, 3x1 + 2x2 ≥ 6, x1 ≤ 1, x2 ≤ 2, x1, x2 ≥ 0. |
| 67. L = 3x1 + 2x2 - 7х3 → min, 4x1 + x2 ≥ 5, 3x2 + 2x3 ≤ 5, 3x1 + x3 ≥ 6, x2 ≥ 13, x3 ≤ 11, x1, x2 ≥ 0. | 68. L = 17x1 - 2x2 - 15х3 → min, 2x1 + x2 ≤ 3, 5x2 + 3x3 ≤ 12, x1 + 2x3 ≥ 4, x2 ≥ 17, x3 ≥ 11, x1, x2 ≥ 0. | 69. L = 6x1 + 5x2 +3х3 → max, 3x1 + 2x3 ≤ 5, x2 + x3 ≤ 2, x1 + 2x2 ≥ 2, x1 ≥ 1, x3 ≥ 2, x1, x2 ≥ 0. |
| 70. L = 5x1 + 3x2 - х3 → min, x1 + 2x3 ≤ 7, 5x2 + 4x3 ≤ 5, 3x1 + x2 ≥ 3, x2 ≥ 5, x3 ≤ 2, x1, x2, х3 ≥ 0. | 71. L = 7x1 + 5x2 + х3 → min, x1 - x2 ≤ 11, x1 + x3 ≤ 2, 2x2 + x3 ≥ 2, x1 ≥ 1, x2 ≥ 5, x1, x2 ≥ 0. | 72. L = x1 + x2 + х3 → max, x1 + x2 ≤ 8, x1 + x3 ≤ 6, x2 + x3 ≥ 3, x2 ≤ 3, x3 ≤ 3, x1, x2 ≥ 0. |
| 73. L = 2x1 + 5x2 + 3х3 → min, 3x1 + x2 ≥ 4, 2x2 + 3x3 ≤ 5, x1 + x3 ≥ 2, x1 ≤ 1, x2 ≥ 2, x1, x2 ≥ 0. | 74. L = 3x1 - 7x2 + 11х3 → max, 6х1 - 2х2 + 5х3 ≥ -5, 8х1 + 9х2 - х3 ≥ 15, х1 - х2 + х3 ≤ 7, х1 ≥ 10, х2 ≥ 10, х2 , х3 ≥ 0. | 75. L = 3x1 + x2 + 5х3 → max, 3x1 - x2 - 2х3 ≥ 4, 2x2 + 4x3 ≤ 3, 6x1 - 3x2 + x3 ≥ 5, x1 ≥ 7, x2 ≥ 9, x1, x2 ≥ 0. |
| 76. L = 8x1 - 42x2 - 13х3 → min, 14х1 + 37х2 + 29х3 ≥ 39, 18х1 - 16х2 - 11х3 ≥ 6, 50х1 + 48х2 + 44х3 ≤ 7, х1 ≥ 19, х3 ≤ 1, х2 , х3 ≥ 0. | 77. L = -0,67x1 – 3,1x2 + 1,9х3 → max, -12x1 + 7x3 ≤ 0,31, 1,2x2 – 1,9x3 ≤ 0,12, 0,13x1 + 1,2x2 ≥ 1,6, x1 ≤ 0,24, x2 ≥ -0,12, x1, х3 ≥ 0. | 78. L = 41x1 + 33x2 + 30х3 → min, 21х1 - 20х2 + 10х3 ≥ -4, 45х1 - 37х2 - 23х3 ≥ 14, 25х1 - 35х2 + 15х3 ≤ 7, -5х2 ≥ 9, х3 ≥ 9, х2 , х3 ≥ 0. |
| 79. L = 2,5x1 – 0,3x2 – 0,6х3 → min, -1,1x1 + 2,5x3 ≤ 7,3, 4,5x2 – 2,4x3 ≤ 5,1, 1,3x1 + 8,5x2 ≥ 3,2, x2 ≥ 5,8, x3 ≤ 2,6, x1, x2, х3 ≥ 0. | 80. L = 71x1 + 67x2 + 9х3 → min, 29x1 + 75x2 ≤ 1, 18x2 + 95x3 ≤ 8, -5x1 + 14x3 ≥ 22, x2 ≥ 87, x3 ≤ 21, x1, x2, х3 ≥ 0. | 81. L = 1,1x1 + 5,2x2 + 3,4х3 → max, 5,2x1 + 7,8x2 ≤ 0,8, 3,7x1 + 9,6x3 ≤ 0,6, 1,9x2 + 4,2x3 ≥ 0,3, x2 ≤ 3,1, x3 ≥ 3,5, x1, x2 ≥ 0. |
| 82. L = 0,41x1 – 0,35x2 + 0,18x3→ max, 1,4x1 – 0,5x2 + 1,6x3 ≤ 0, 5,4x1 + 3,7x2 + 1,3x3 ≤ 1,7, 2,1x1 + x2 ≥ 2,5, x1 ≥ 1,3, 0,7x2 ≤ 8,2, x1, x3 ≥ 0. | 83. L = 77x1 - 99x2 + 83х3 – 69x4 → min, -57x1 + 49x2 - 11х3 + 73x4 ≥ 81, 86x1 - 72x2 + 77х3 – 33x4 ≤ 29, -37x1 + 47x2 + 13х3 + 41x4 ≥ 34, 45x1 - 34x2 + 85x3 - 23x4 ≤ 89, x1, x2, x3, x4 ≥ 0. | 84. L = -2,5x1 – 6,5x2 + 1,2x3→ max, 5,9x1 + 6,3x2 + 9,7x3 ≥ 1,2, -0,2x1 - x2 + x3 ≤ 3,8, -x1 + 3,2x2 + x3 ≤ 2,5, x1 ≥ 1,1, x2 ≤ 1,2, x1, x3 ≥ 0. |
| 85. L = 0,61x1 – 0,75x2 – 1,8x3→ max, -1,7x1 – 0,33x2 + 1,7x3 ≤ 0,3, 6,13x1 + 0,7x2 + 1,5x3 ≤ 2,7, -2,7x1 + 3,8x2 ≥ 2,4, x2 ≥ 0,23, 0,7x3 ≥ 0,25, x1, x3 ≥ 0. | 86. L = 17x1 - 38x2 - 22х3 – 91x4 → min, 16x1 - 11x2 + 13х3 + 47x4 ≥ 36, 49x1 + 37x2 - 53х3 + 11x4 ≥ 45, 14x1 + 83x2 + 6х3 + 5x4 ≤ 49, 55x1 - 21x2 + 39x3 + 42x4 ≤ 63, x1, x2, x3, x4 ≥ 0. | 87. L = 0,3x1 + 1,5x2 - 1,3x3→ max, -0,19x1 + 0,31x2 + 0,17x3 ≥ 1,2, -0,25x1 – 2,8x2 + 3,7x3 ≤ 6,3, -7,27x1 + 3,21x2 - 0,89x3 ≤ 2,7, x1 ≥ 0,1, x2 ≤0,3, x1, x3 ≥ 0. |
| 88. L = 43x1 + 72x2 + 21х3 + 54x4 → max, 29x1 + 44x2 + 96х3 + 85x4 ≥ 34, 67x1 - 98x2 - 42х3 – 31x4 ≤ 23, 39x1 - 96x2 - 22х3 + 75x4 ≥ 56, 67x1 + 93x2 - 86x3 + 67x4 ≤ 59, x1, x2, x3, x4 ≥ 0. | 89. L = -4x1 - 2x2 + 5х3 → max, -2х1 - 2х2 - 5х3 ≥ -5, -3х1 - 7х2 – 9х3 ≥ 15, 12х1 - 8х2 - 4х3 ≤ 7, х2 ≤ 15, х3 ≥ 6, х1 , х3 ≥ 0. | 90. L = 38x1 - 26x2 + 11х3 – 19x4 → max, 30x1 + 27x2 - 41х3 - 16x4 ≥ 26, 99x1 - 76x2 + 32х3 – 12x4 ≤ 37, 74x1 + 80x2 - 43х3 + 31x4 ≤ 50, 20x1 - 22x2 + 65x3 - 71x4 ≤ 82, x1, x2, x3, x4 ≥ 0. |
| 91. L = 8x1 + 67x2 + 35х3 → min, 25x1 + 76x2 ≤ 73, 5x2 + 16x3 ≤ 41, -49x1 + 3x3 ≥ 3, x2 ≥ 5, x3 ≤ 2, x1, x2, х3 ≥ 0. | 92. L = 21x1 + 14x2 - 3х3 → min, 51x1 - 6x2 + 13x3 ≤ 18, 26x2 - 20x3 ≤ 31, 43x1 + 46x2 – 13x3 ≥ 3, x2 ≤ 40, x3 ≤ 6, x1, x2, х3 ≥ 0. | 93. L = 4x1 - 31x2 - 19х3 → min, -12x1 + 7x3 ≤ 3, 12x2 + 19x3 ≤ 2, 13x1 + 12x2 ≥ 6, x1 ≤ 2, x2 ≥ 12, x1, x2, х3 ≥ 0. |
| 94. L = 18x1 + 2x2 - 9х3 → min, 37x1 + 56x2 + 33x3 ≤ 40, - x1 - 14x2 + 22x3 ≤ 15, 3x1 + 7x2 + 3x3≥ 1, x1 ≥ 6, x2 ≤ 1, x1, x2, х3 ≥ 0. | 95. L = 17x1 - 9x2 - 10х3 → min, -28x1 + 21x2 + 5x3 ≤ 8, -11x1 + 3x2 + 7x3 ≤ 6, 7x1 + 34x2 - 36x3 ≥ 3, x2 ≥ 16, x3 ≤ 19, x1, x2, х3 ≥ 0. | 96. L = -49x1 - 22x2 +5х3 → min, 14x1 - 42x3 ≤ 21, 38x2 – 13x3 ≤ 2, 18x1 – 52x2 ≥ 2, x1 ≥ 9, x3 ≤ 2, x1, x2, х3 ≥ 0. |
| 97. L = x1 - 3x2 + 2x3→ min, 6x1 + 7x2 ≤ 9, 3x2 + 5x3 ≥ 6, 5x1 + 3x3 ≥ 11, 7x1 ≥ 1, 5x2 ≤ 18, x1, x3 ≥ 0. | 98. L = 25x1 + 5x2 + 12x3→ max, 5x1 +3x2 + 7x3 ≥ 12, 2x1 - x2 + x3 ≤ 8, -x1 + 2x2 + x3 ≤ 5, x1 ≥ 11, x2 ≤ 12, x1, x3 ≥ 0. | 99. L = -x1 - 3x2 + 6x3→ max, 5x1 + 3x3 ≥ 15, -4x2 + x3 ≥ 5, 3x1 – x3 ≤ 7, 5x1 ≥ 1, x2 ≤ 18, x2, x3 ≥ 0. |
| 100. L = 41x1 - 35x2 + 18x3→ max, 14x1 - 5x2 + 16x3 ≤ 0, 4x1 + 7x2 + 13x3 ≤ 1, 2x1 + x2 ≥ 25, 3x1 ≥ 1, 7x2 ≤ 8, x1, x3 ≥ 0. |