Решение поставленной задачи
Условие задачи
В состав рациона кормления входят три продукта: сено, силос и концентраты, содержащие питательные вещества: белок, кальций, витамины. Содержание питательных веществ соответствующего продукта питания и минимально необходимые нормы их потребления заданы таблицей:
Таблица 4.1
Продукты
| Питательные вещества
|
Белок
| Кальций
| Витамины
|
Сено
| 50
| 6
| 2
|
Силос
| 20
| 4
| 1
|
Концентраты
| 180
| 3
| 1
|
Нормы потребления
| 2000
| 120
| 40
|
Используя эти данные, решить следующие задачи:
1 Определить оптимальный рацион кормления из условия минимальной стоимости, если цена 1 кг продукта питания соответственно составляет: сена –3 коп., силоса – 2 коп., и концентратов – 5 коп.
2. Решить задачу 1, если заданы дополнительные предельные нормы суточной выдачи: сена не более 12 кг, силоса – не более 20 кг и концентратов – не более 16 кг.
3. Включить в задачу 2 условие ограниченности ресурсов продуктов на один рацион: сена – не более 10 кг, силоса – не более 15 кг и концентратов – не более 20 кг.
4. Определить влияние на оптимальную стоимость рациона увеличения ресурсов сена и силоса на 1 кг и концентратов на 3 кг.
5. В найденном (в задаче 2) оптимальном рацион заменить 1 кг сена на силос или концентраты. Определить, при какой замене минимальная стоимость измениться наименьшим образом.
Решение задачи в ручную
Задача 1
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Приведем задачу у виду удобному для решения
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Заполним симплекс – таблицу
Таблица 4.2
№
| Базис
| С
| План
| 3
| 2
| 5
| 0
| 0
| 0
| М
| М
| М
|
|
|
|
|
|
|
|
|
|
I
| 
| М
| 2000
| 50
| 20
| <180>
| -1
| 0
| 0
| 1
| 0
| 0
|

| М
| 120
| 6
| 4
| 3
| 0
| -1
| 0
| 0
| 1
| 0
|

| М
| 40
| 2
| 1
| 1
| 0
| 0
| -1
| 0
| 0
| 1
|

|
| 0
| -3
| -2
| -5
| 0
| 0
| 0
| 0
| 0
| 0
|
М
|
| 2160
| 58
| 25
| 184
| -1
| -1
| -1
| 0
| 0
| 0
|
II
| 
| 5
| 11.11
| 0.28
| 0.11
| 1
| -0.006
| 0
| 0
|
| 0
| 0
|

| М
| 86.67
| <5.17>
| 3.67
| 0
| 0.017
| -1
| 0
| 1
| 0
|

| М
| 28.89
| 1.72
| 0.89
| 0
| 0.006
| 0
| -1
| 0
| 1
|

|
| 55.55
| -1.6
| -1.45
| 0
| -0.03
| 0
| 0
| 0
| 0
|
М
|
| 115.56
| 6.89
| 4.56
| 0
| 0.23
| -1
| -1
| 0
| 0
|
№
| Базис
| С
| План
| 3
| 2
| 5
| 0
| 0
| 0
| М
| М
| М
|
|
|
|
|
|
|
|
|
|
III
|
| 5
| 6.45
| 0
| -0.03
| 1
| -0.006
| 0
| 0.17
|
| 0.07
|
|
| М
| 0
| 0
| 1
| 0
| 0
| -1
| <3>
| 0
|
| 3
| 16.77
| 1
| 0.51
| 0
| 0.003
| 0
| -0.58
| -0.003
|
|
| 82.56
| 0
| -0.62
| 0
| -0.021
|
|
| 0.34
|
М
|
| 0
| 0
| 1
| 0
| 0
| -1
| 3
| 0
|
IV
|
| 5
| 6.45
| 0
| -0.09
| 1
| -0.007
| 0.054
| 0
|
|
|
|
| 0
| 0
| 0
| 0.33
| 0
| 0
| -0.33
| 1
|
| 3
| 16.77
| 1
| 0.71
| 0
| 0.003
| -0.19
| 0
|
|
| 82.58
| 0
| -0.3
| 0
| -0.023
| -0.31
| 0
|
| | | | | | | | | | | | | |
Оптимальный рацион для скота включает корма: сена – 16.77, концентратов – 6.45. Стоимость рациона составила 82.58 копеек.
Задача 2
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Приведем задачу у виду удобному для решения

Заполним симплекс – таблицу
Таблица 4.3
Учитывая предельные нормы суточной выдачи оптимальный рацион для скота будет включать в себя корма: сено – 12, силос – 9.25, концентраты – 6.25. При чем остаются недоиспользованные ресурсы по силосу в размере 10.75 и по концентратам – 9.25. В этом случае стоимость рациона составила 88.25 копеек.
Задача 3


Приведем задачу у виду удобному для решения

Заполним симплекс – таблицу
Таблица 4.4
№
| Базис
| С
| План
| 3
| 2
| 5
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| М
| М
| М
|
| 
| 
| 
|
| 
| 
| 
| 
|
|
|
|
|
|
|
I
| 
| М
| 2000
| 50
| 20
| <180>
| -1
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 1
| 0
| 0
|

| М
| 120
| 6
| 4
| 3
| 0
| -1
| 0
| 0
| 1
| 0
| 0
| 0
| 0
| 0
| 1
| 0
|

| М
| 40
| 2
| 1
| 1
| 0
| 0
| -1
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 1
|

| 0
| 12
| 1
| 0
| 0
| 0
| 0
| 0
| 1
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
|

| 0
| 20
| 0
| 1
| 0
| 0
| 0
| 0
| 0
| 1
| 0
| 0
| 0
| 0
| 0
| 0
| 0
|

| 0
| 16
| 0
| 0
| 1
| 0
| 0
| 0
| 0
| 0
| 1
| 0
| 0
| 0
| 0
| 0
| 0
|

| 0
| 10
| 1
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 1
| 0
| 0
| 0
| 0
| 0
|

| 0
| 15
| 0
| 1
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 1
| 0
| 0
| 0
| 0
|

| 0
| 20
| 0
| 0
| 1
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 1
| 0
| 0
| 0
|

|
| 0
| -3
| -2
| -5
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
|
М
|
| 2160
| 58
| 25
| 184
| -1
| -1
| -1
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
|
II
| 
| 5
| 11.11
| 0.28
| 0.11
| 1
| -0.006
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
|
| 0
| 0
|

| М
| 86.67
| 5.17
| 3.67
| 0
| 0.017
| -1
| 0
| 0
| 1
| 0
| 0
| 0
| 0
| 1
| 0
|

| М
| 28.89
| 1.72
| 0.89
| 0
| 0.006
| 0
| -1
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 1
|

| 0
| 12
| 1
| 0
| 0
| 0
| 0
| 0
| 1
| 0
| 0
| 0
| 0
| 0
| 0
| 0
|

| 0
| 20
| 0
| 1
| 0
| 0
| 0
| 0
| 0
| 1
| 0
| 0
| 0
| 0
| 0
| 0
|

| 0
| 4.89
| -0.28
| -0.11
| 0
| 0.006
| 0
| 0
| 0
| 0
| 1
| 0
| 0
| 0
| 0
| 0
|

| 0
| 10
| <1>
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 1
| 0
| 0
| 0
| 0
|

| 0
| 15
| 0
| 1
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 1
| 0
| 0
| 0
|

| 0
| 8.89
| -0.28
| -0.11
| 0
| 0.006
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 1
| 0
| 0
|

|
| 55.55
| -1.6
| -1.45
| 0
| -0.03
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
|
М
|
| 115.56
| 6.89
| 4.56
| 0
| 0.023
| 0
| -1
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
|
№
| Базис
| С
| План
| 3
| 2
| 5
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| М
| М
| М
|

|
| 
| 
| 
|
|
| 
| 
| 
|
|
|
|
|
|
III
| 
| 5
| 8.33
| 0
| 0.11
| 1
| -0.006
| 0
| 0
| 0
| 0
| 0
| -0.28
| 0
| 0
|
| 0
| 0
|

| М
| 35
| 0
| <3.67>
| 0
| 0.017
| -1
| 0
| 0
| 0
| 0
| -5.17
| 0
| 0
| 1
| 0
|

| М
| 11.67
| 0
| 0.89
| 0
| 0.06
| 0
| -1
| 0
| 0
| 0
| -1.72
| 0
| 0
| 0
| 1
|

| 0
| 2
| 0
| 0
| 0
| 0
| 0
| 0
| 1
| 0
| 0
| -1
| 0
| 0
| 0
| 0
|

| 0
| 20
| 0
| 1
| 0
| 0
| 0
| 0
| 0
| 1
| 0
| 0
| 0
| 0
| 0
| 0
|

| 0
| 7.67
| 0
| -0.11
| 0
| 0.006
| 0
| 0
| 0
| 0
| 1
| 0.28
| 0
| 0
| 0
| 0
|

| 3
| 10
| 1
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 1
| 0
| 0
| 0
| 0
|

| 0
| 15
| 0
| 1
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 1
| 0
| 0
| 0
|

| 0
| 11.67
| 0
| -0.11
| 0
| 0.006
| 0
| 0
| 0
| 0
| 0
| 0.28
| 0
| 1
| 0
| 0
|

|
| 71.65
| 0
| -1.45
| 0
| -0.03
| 0
| 0
| 0
| 0
| 0
| 1..65
| 0
| 0
| 0
| 0
|
М
|
| 46.67
| 0
| 4.56
| 0
| 0.023
| -1
| -1
| 0
| 0
| 0
| -6.89
| 0
| 0
| 0
| 0
|
IV
| 
| 5
| 7.27
| 0
| 0
| 1
| -0.06
| 0.03
| 0
| 0
| 0
| 0
| -0.12
| 0
| 0
|
| 0
| 0
|

| 2
| 9.54
| 0
| 1
| 0
| 0.004
| -0.28
| 0
| 0
| 0
| 0
| -1.41
| 0
| 0
| 0
|

| М
| 3.18
| 0
| 0
| 0
| 0.001
| <0.24>
| -1
| 0
| 0
| 0
| -0.47
| 0
| 0
| 1
|

| 0
| 2
| 0
| 0
| 0
| 0
| 0
| 0
| 1
| 0
| 0
| -1
| 0
| 0
| 0
|

| 0
| 10.45
| 0
| 0
| 0
| -0.04
| 0.28
| 0
| 0
| 1
| 0
| 1.41
| 0
| 0
| 0
|

| 0
| 8.73
| 0
| 0
| 0
| 0.006
| -0.03
| 0
| 0
| 0
| 1
| 0.12
| 0
| 0
| 0
|

| 3
| 10
| 1
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 0
| 1
| 0
| 0
| 0
|

| 0
| 5.45
| 0
| 0
| 0
| -0.04
| 0.28
| 0
| 0
| 0
| 0
| 1.41
| 1
| 0
| 0
|

| 0
| 12.73
| 0
| 0
| 0
| 0.06
| -0.03
| 0
| 0
| 0
| 0
| 0.12
| 0
| 1
| 0
|

|
| 85,43
| 0
| 0
| 0
| -0,022
| -0.37
| 0
| 0
| 0
| 0
| 1.46
| 0
| 0
| 0
|
М
|
| 3.18
| 0
| 0
| 0
| 0.001
| 0.24
| -1
| 0
| 0
| 0
| -0.47
| 0
| 0
| 0
|
V
| 
| 5
| 6.88
| 0
| 0
| 1
| -0.006
| 0
| 0.12
| 0
| 0
| 0
| -0.063
| 0
| 0
|
|
|
|

| 2
| 13.12
| 0
| 1
| 0
| 0.006
| 0
| -1.12
| 0
| 0
| 0
| -1.94
| 0
| 0
|

| 0
| 13.12
| 0
| 0
| 0
| 0.006
| 1
| -4.12
| 0
| 0
| 0
| -1.94
| 0
| 0
|

| 0
| 2
| 0
| 0
| 0
|
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