Реферат: Исследование математических операций
2 шаг
, где
В ходе преобразований имеем:
Строим симплекс таблицу:
Итерация 0
Базис | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | Решение | Оценка | |
![]() | 15 | 15 | -1 | 0 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | 34 | |
![]() | -2 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 6 | 6 |
![]() | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 6 | - |
![]() | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 7 | 7 |
![]() ![]() | 1 | 7 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 7 | 1![]() |
![]() | 2 | 5 | 0 | 0 | -1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 10 | 2 |
![]() | 5 | 2 | 0 | 0 | 0 | -1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 10 | 5 |
![]() | 7 | 1 | 0 | 0 | 0 | 0 | -1 | 0 | 0 | 0 | 0 | 0 | 1 | 7 | 7 |
- ведущий столбец
- ведущая строка
Итерация 1
Базис | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | Решение | Оценка | |
![]() | 12,8571 | 0 | 1,1429 | 0 | -1 | -1 | -1 | 0 | 0 | -2,1429 | 0 | 0 | 0 | 19 | |
![]() | -2,1429 | 0 | 0,1429 | 1 | 0 | 0 | 0 | 0 | 0 | -0,1429 | 0 | 0 | 0 | 5 | - |
![]() | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 6 | 6 |
![]() | -0,1429 | 0 | 0,1429 | 0 | 0 | 0 | 0 | 0 | 1 | -0,1429 | 0 | 0 | 0 | 6 | - |
![]() | 0,1429 | 1 | -0,1429 | 0 | 0 | 0 | 0 | 0 | 0 | 0,1429 | 0 | 0 | 0 | 1 | 7 |
![]() | 1,2857 | 0 | 0,7143 | 0 | -1 | 0 | 0 | 0 | 0 | -0,7143 | 1 | 0 | 0 | 5 | 3,8889 |
![]() | 4,7143 | 0 | 0,2857 | 0 | 0 | -1 | 0 | 0 | 0 | -0,2857 | 0 | 1 | 0 | 8 | 1,697 |
![]() ![]() | 6,8571 | 0 | 0,1429 | 0 | 0 | 0 | -1 | 0 | 0 | -0,1429 | 0 | 0 | 1 | 6 | 0,875![]() |
- ведущий столбец
- ведущая строка
Итерация 2
Базис | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | Решение | Оценка | |
![]() | 0 | 0 | 0,875 | 0 | -1 | -1 | 0,875 | 0 | 0 | -1,875 | 0 | 0 | -1,875 | 7,75 | |
![]() | 0 | 0 | 0,1875 | 1 | 0 | 0 | -0,3125 | 0 | 0 | -0,1875 | 0 | 0 | 0,3125 | 6,875 | 36,6667 |
![]() | 0 | 0 | -0,0208 | 0 | 0 | 0 | 0,1458 | 1 | 0 | 0,0208 | 0 | 0 | -0,1458 | 5,125 | - |
![]() | 0 | 0 | 0,1458 | 0 | 0 | 0 | -0,0208 | 0 | 1 | -0,1458 | 0 | 0 | 0,0208 | 6,125 | 42 |
![]() | 0 | 1 | -0,1458 | 0 | 0 | 0 | 0,0208 | 0 | 0 | 0,1458 | 0 | 0 | -0,0208 | 0,875 | - |
![]() ![]() | 0 | 0 | 0,6875 | 0 | -1 | 0 | 0,1875 | 0 | 0 | -0,6875 | 1 | 0 | -0,1875 | 3,875 | 5,6364![]() |
![]() | 0 | 0 | 0,1875 | 0 | 0 | -1 | 0,6875 | 0 | 0 | -0,1875 | 0 | 1 | -0,6875 | 3,875 | 20,6666 |
![]() | 1 | 0 | 0,0208 | 0 | 0 | 0 | -0,1458 | 0 | 0 | -0,0208 | 0 | 0 | 0,1458 | 0,875 | 42 |
- ведущий столбец
- ведущая строка
Итерация 3
Базис | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | Решение | Оценка | |
![]() | 0 | 0 | 0 | 0 | 0,2727 | -1 | 0,6364 | 0 | 0 | -1 | -1,2727 | 0 | -1,6364 | 2,8182 | |
![]() | 0 | 0 | 0 | 1 | 0,2727 | 0 | -0,3636 | 0 | 0 | 0 | -0,2727 | 0 | 0,3636 | 5,8182 | - |
![]() | 0 | 0 | 0 | 0 | -0,0303 | 0 | 0,1515 | 1 | 0 | 0 | 0,0303 | 0 | -0,1515 | 5,2422 | 34,6009 |
![]() | 0 | 0 | 0 | 0 | 0,2121 | 0 | -0,0606 | 0 | 1 | 0 | -0,2121 | 0 | 0,0606 | 5,3033 | - |
![]() | 0 | 1 | 0 | 0 | -0,2121 | 0 | 0,0606 | 0 | 0 | 0 | 0,2121 | 0 | -0,0606 | 1,6967 | 27,9978 |
![]() | 0 | 0 | 1 | 0 | -1,4545 | 0 | 0,2727 | 0 | 0 | -1 | 1,4545 | 0 | -0,2727 | 5,6364 | 20,6670 |
![]() ![]() | 0 | 0 | 0 | 0 | 0,2727 | -1 | 0,6364 | 0 | 0 | 0 | -0,2727 | 1 | -0,6364 | 2,8182 | 4,4285![]() |
![]() | 1 | 0 | 0 | 0 | 0,0303 | 0 | -0,1515 | 0 | 0 | 0 | -0,0303 | 0 | 0,1515 | 0,7578 | - |
- ведущий столбец
- ведущая строка
Итерация 4
Базис | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | Решение |
![]() | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | 0 |
![]() | 0 | 0 | 0 | 1 | 0,4285 | -0,5713 | 0 | 0 | 0 | 0 | -0,4285 | 0,5713 | 0 | 7,4283 |
![]() | 0 | 0 | 0 | 0 | -0,0952 | 0,2381 | 0 | 1 | 0 | 0 | 0,0952 | -0,2381 | 0 | 4,5714 |
![]() | 0 | 0 | 0 | 0 | 0,238 | -0,0952 | 0 | 0 | 1 | 0 | -0,238 | 0,0952 | 0 | 5,5716 |
![]() | 0 | 1 | 0 | 0 | -0,238 | 0,0952 | 0 | 0 | 0 | 0 | 0,238 | -0,0952 | 0 | 1,4284 |
![]() | 0 | 0 | 1 | 0 | -1,5714 | 0,4285 | 0 | 0 | 0 | -1 | 1,5714 | -0,4285 | 0 | 4,4288 |
![]() | 0 | 0 | 0 | 0 | 0,4285 | -1,5713 | 1 | 0 | 0 | 0 | -0,4285 | 1,5713 | -1 | 4,4283 |
![]() | 1 | 0 | 0 | 0 | 0,0952 | -0,2381 | 0 | 0 | 0 | 0 | -0,0952 | 0,2381 | 0 | 1,4286 |
Полученная симплекс-таблица удовлетворяет условиям оптимальности и допустимости.
Переходим на на 2 этап двухэтапного метода