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Консультация № 198703
24.05.2020, 16:36
0.00 руб.
1
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1
Здраствуйте! у меня возникли сложности с решением следующей задачи. Имеется приложение
Прикрепленные файлы:
Обсуждение
20.08.2022, 13:28
общий
20.08.2022, 13:37
это ответ
Здравствуйте, av_maly20!
Требуется решить графическим методом задачу линейного программирования. Найти минимум функции
при следующих ограничениях:
Для решения задачи используем методику, изложенную в [1, с. 117-118]. В используемых в этой методике обозначениях целевая функция будет такой:
Воспользуемся Интернет-ресурсом для построения многоугольника решений. При этом примем обозначения 
В результате получим четырёхугольник 
(рисунок с графиком находится в первом прикреплённом файле). На графике показаны линия уровня 
и вектор 
Перемещая линию уровня в направлении, противоположном направлению вектора 
установим, что наименьшего значения целевая функция достигает при совпадении с параллельной ей прямой 
При этом 
поскольку 
Ответ: минимум целевой функции равен минус 6.
Для проверки полученного решения я воспользовался Интернет-ресурсом Ссылка >>. Полученное решение показано во втором и следующих прикреплённых файлах.
Литература
1 Черненко В. Д. Высшая математика в примерах и задачах. В 3 т.: Т. 3. - СПб.: Политехника, 2003.
Требуется решить графическим методом задачу линейного программирования. Найти минимум функции
при следующих ограничениях:Для решения задачи используем методику, изложенную в [1, с. 117-118]. В используемых в этой методике обозначениях целевая функция будет такой:
Воспользуемся Интернет-ресурсом для построения многоугольника решений. При этом примем обозначения В результате получим четырёхугольник (рисунок с графиком находится в первом прикреплённом файле). На графике показаны линия уровня и вектор Перемещая линию уровня в направлении, противоположном направлению вектора установим, что наименьшего значения целевая функция достигает при совпадении с параллельной ей прямой При этом поскольку Ответ: минимум целевой функции равен минус 6.
Для проверки полученного решения я воспользовался Интернет-ресурсом Ссылка >>. Полученное решение показано во втором и следующих прикреплённых файлах.
Литература
1 Черненко В. Д. Высшая математика в примерах и задачах. В 3 т.: Т. 3. - СПб.: Политехника, 2003.
Прикрепленные файлы:
Об авторе:
Facta loquuntur.
Facta loquuntur.
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