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Консультация № 182228
15.02.2011, 22:49
55.00 руб.
16.02.2011, 07:43
0
5
1
Здравствуйте! Прошу помощи в следующем вопросе:
Необходимо решить задачу линейного программирования графически:
L = x1 + x2 → max
x1 + 2•x2 <= 10
x1 + 2•x2 >= 2
2•x1 + x3 <= 10
x1 >=0, x2 >=0
Смущает меня x3.
Заранее спасибо.
Необходимо решить задачу линейного программирования графически:
L = x1 + x2 → max
x1 + 2•x2 <= 10
x1 + 2•x2 >= 2
2•x1 + x3 <= 10
x1 >=0, x2 >=0
Смущает меня x3.
Заранее спасибо.
Обсуждение
15.02.2011, 22:55
общий
Согласен с Гаряка Асмик. Графическим методом в трехмерном пространстве не решают.
Неизвестный
15.02.2011, 23:36
общий
Адресаты:
Огромное спасибо за ответ!
Хотелось бы уточнить почему заштрихована именно эта область на рисунке и как получилось, что x1= 10/3 и x2=10/3.
Спасибо.
Хотелось бы уточнить почему заштрихована именно эта область на рисунке и как получилось, что x1= 10/3 и x2=10/3.
Спасибо.
15.02.2011, 23:43
общий
Координаты точки М находятся из системы уравнений (пересечение прямых) - решена справа от рисунка.
Область получается из трех пяти ограничений (неравенств) :
x1 + 2x2 <= 10
x1 + 2x2 >= 2
2x1 + x2 <= 10
x1 >=0
x2 >=0
Грубо говоря, заключена между прямыми (если неравенства заменить равенствами)
Чтобы найти точку максимума, надо прямую, перпендикулярную к вектору N (координаты которого есть коэффициентами целевой функции) перемещать параллельно в направлении этого вектора. Точка, в которой произойдет последнее соприкасание прямой с областью, и будет точкой максимума. В нашем случае это точка М.
Область получается из трех пяти ограничений (неравенств) :
x1 + 2x2 <= 10
x1 + 2x2 >= 2
2x1 + x2 <= 10
x1 >=0
x2 >=0
Грубо говоря, заключена между прямыми (если неравенства заменить равенствами)
Чтобы найти точку максимума, надо прямую, перпендикулярную к вектору N (координаты которого есть коэффициентами целевой функции) перемещать параллельно в направлении этого вектора. Точка, в которой произойдет последнее соприкасание прямой с областью, и будет точкой максимума. В нашем случае это точка М.
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