Курсовая работа: Линейное и нелинейное программирование
x1 ↑F↓ x4 ↑F↑ Выбираем x1 ↔ x5
x1 , x2 , x3 , x6 - базисные переменные, x4 , x5 – свободные переменные
x1 ↑F↑ x4 ↑F↑
X=(2, 4, 7, 0, 0, 5)
F = -14
2.1.5 Метод симплекс-таблицы
Приведем к каноническому виду:
x2 , x4 , x5 , x6 – базисные переменные, x1 , x3 – свободные переменные
| ↑ | |||||
| b | x1 | x3 | |||
| x2 | 1 | 2 | -1 | ||
| 1 | -3 | 1 | |||
| ← | x4 | 1 | -3 | 1 | 1 |
| 1 | -3 | 1 | |||
| x5 | 12 | -1 | 2 | 6 | |
| -2 | 6 | -2 | |||
| x6 | 4 | 3 | -1 | ||
| 1 | -3 | 1 | |||
| F | -4 | -9 | 4 | ||
| -4 | 12 | -4 | |||
| ↑ | |||||
| b | x1 | x4 | |||
| x2 | 2 | -1 | 1 | ||
| 2 | 1/5 | -2/5 | |||
| x3 | 1 | -3 | 1 | ||
| 6 | 3/5 | -6/5 | |||
| ← | x5 | 10 | 5 | -2 | 2 |
| 2 | 1/5 | -2/5 | |||
| x6 | 5 | 0 | 1 | ||
| 0 | 0 | 0 | |||
| F | -8 | 3 | -4 | ||
| -6 | -3/5 | 6/5 | |||
| b | x5 | x4 | |||
| x2 | 4 | 1/5 | 3/5 | ||
| x3 | 7 | 3/5 | -1/5 | ||
| x1 | 2 | 1/5 | -2/5 | ||
| x6 | 5 | 0 | 1 | ||
| F | -14 | -3/5 | -14/5 | ||
X = (2, 4, 7, 0, 0, 5)
F = -14 
2.1.6 Метод допустимого базиса
| ↑ | |||||||||||||
| b | x1 | x2 | x3 | x4 | x5 | x6 | |||||||
| F | 0 | -1 | 4 | 0 | 0 | 0 | 0 | ||||||
| 1/2 | 1/2 | 1/2 | -1/2 | 0 | 0 | 0 | |||||||
| ← | ξ1 | 1 | 2 | 1 | -1 | 0 | 0 | 0 | 1/2 | ||||
| 1/2 | 1/2 | 1/2 | -1/2 | 0 | 0 | 0 | |||||||
| ξ2 | 2 | -1 | 1 | 0 | 1 | 0 | 0 | 14/3 | |||||
| 1/2 | 1/2 | 1/2 | -1/2 | 0 | 0 | 0 | |||||||
| ξ3 | 14 | 3 | 2 | 0 | 0 | 1 | 0 | 3 | |||||
| -3/2 | -3/2 | -3/2 | 3/2 | 0 | 0 | 0 | |||||||
| ξ4 | 3 | 1 | -1 | 0 | 0 | 0 | 1 | ||||||
| -1/2 | -1/2 | -1/2 | 1/2 | 0 | 0 | 0 | |||||||
| f | 20 | 5 | 3 | -1 | 1 | 1 | 1 | ||||||
| -5/2 | -5/2 | -5/2 | 5/2 | 0 | 0 | 0 | |||||||
| ↑ | |||||||||||||
| b | ξ1 | x2 | x3 | x4 | x5 | x6 | |||||||
| F | 1/2 | 1/2 | 9/2 | -1/2 | 0 | 0 | 0 | ||||||
| 5/2 | -1/2 | -3/2 | 1 | 0 | 0 | 1 | |||||||
| x1 | 1/2 | 1/2 | 1/2 | -1/2 | 0 | 0 | 0 | ||||||
| 5/2 | -1/2 | -3/2 | 1 | 0 | 0 | 1 | |||||||
| ξ2 | 5/2 | 1/2 | 3/2 | -1/2 | 1 | 0 | 0 | ||||||
| 5/2 | -1/2 | -3/2 | 1 | 0 | 0 | 1 | |||||||
| ξ3 | 25/2 | -3/2 | 1/2 | 3/2 | 0 | 1 | 0 | 25/3 | |||||
| -15/2 | 3/2 | 9/2 | -3 | 0 | 0 | -3 | |||||||
| ← | ξ4 | 5/2 | -1/2 | -3/2 | 1/2 | 0 | 0 | 1 | 5 | ||||
| 5 | -1 | -3 | 2 | 0 | 0 | 2 | |||||||
| f | 35/2 | -5/2 | 1/2 | 3/2 | 1 | 1 | 1 | ||||||
| -15/2 | 3/2 | 9/2 | -3 | 0 | 0 | -3 | |||||||
| ↑ | |||||||||||||
| b | ξ1 | x2 | ξ4 | x4 | x5 | x6 | |||||||
| F | 3 | 0 | 3 | 1 | 0 | 0 | 1 | ||||||
| -3 | 0 | -3/5 | 9/5 | 0 | -3/5 | 9/5 | |||||||
| x1 | 3 | 0 | -1 | 1 | 0 | 0 | 1 | ||||||
| 1 | 0 | 1/5 | -3/5 | 0 | 1/5 | -3/5 | |||||||
| ξ2 | 5 | 0 | 0 | 1 | 1 | 0 | 1 | ||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||||
| ← | ξ3 | 5 | 0 | 5 | -3 | 0 | 1 | -3 | 1 | ||||
| 1 | 0 | 1/5 | -3/5 | 0 | 1/5 | -3/5 | |||||||
| x3 | 5 | -1 | -3 | 2 | 0 | 0 | 2 | ||||||
| 3 | 0 | 3/5 | -9/5 | 0 | 3/5 | -9/5 | |||||||
| f | 10 | -1 | 5 | -3 | 1 | 1 | -2 | ||||||
| -5 | 0 | -1 | 3 | 0 | -1 | 3 | |||||||
| ↑ | |||||||||||||
| b | ξ1 | ξ3 | ξ4 | x4 | x5 | x6 | |||||||
| F | 0 | 0 | -3/5 | 14/5 | 0 | -3/5 | 14/5 | ||||||
| -14 | 0 | 0 | -14/5 | -14/5 | 0 | -14/5 | |||||||
| x1 | 4 | 0 | 1/2 | 2/5 | 0 | 1/5 | 2/5 | 10 | |||||
| -2 | 0 | 0 | -2/5 | -2/5 | 0 | -2/5 | |||||||
| ← | ξ2 | 5 | 0 | 0 | 1 | 1 | 0 | 1 | 5 | ||||
| 5 | 0 | 0 | 1 | 1 | 0 | 1 | |||||||
| x2 | 1 | 0 | 1/5 | -3/5 | 0 | 1/5 | -3/5 | ||||||
| 3 | 0 | 0 | 3/5 | 3/5 | 0 | 3/5 | |||||||
| x3 | 8 | -1 | 3/5 | 1/5 | 0 | 3/5 | 1/5 | 40 | |||||
| -1 | 0 | 0 | -1/5 | -1/5 | 0 | -1/5 | |||||||
| f | 5 | -1 | -1 | 0 | 1 | 0 | 1 | ||||||
| -5 | 0 | 0 | -1 | -1 | 0 | -1 | |||||||
 |  | | |||||||||||
| b |  ξ1 | ξ3 | ξ4 | x4 | x5 | ξ2 | |||||||
| F | -14 | 0 | -3/5 | 0 | -14/5 | -3/5 | -14/5 | ||||||
| x1 | 2 | 0 | 1/5 | 0 | -2/5 | 1/5 | -2/5 | ||||||
| x6 | 5 | 0 | 0 | 1 | 1 | 0 | 1 | ||||||
| x2 | 4 | 0 | 1/5 | 0 | 3/5 | 1/5 | -3/5 | ||||||
| x3 | 7 | -1 | 3/5 | 0 | -1/5 | 3/5 | -1/5 | ||||||
 | f | 0 | -1 | -1 | -1 | 0 | 0 | -1 | |||||
| b | x4 | x5 | |
|
F |
-14 | -14/5 | -3/5 |
| x6 |
5 | 1 | 0 |
| x2 |
4 | 3/5 | 1/5 |
| x3 |
7 | -1/5 | 3/5 |
| x1 |
2 |
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