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Задача из раздела "Нелинейное программирование" Постановка задачи. Предприятие производит продукцию по двум технологическим способам производства. Для производства продукции используется сырье двух видов, объемы которых у предприятия составляют b1 и b2 ед. Оптовая цена единицы продукции по 1-му и 2-му способам производства составляют соответственно P1 и Р2 денежных единиц. Себестоимость производства по 1-му и 2-му способам определяется выражениями cj= cj’ + cj’’хj, j= 1, 2. Нормы расхода ресурсов, затрачиваемых на производство единицы продукции по каждому технологическому способу, равны aij. Необходимо построить математическую модель задачи и определить, сколько продукции нужно производить по каждому из технологических способов, чтобы получить максимум прибыли. Исходные данные для решения задачи представлены в таблице 1. Таблица 1 – Исходные данные № задачи b1 b2 P1 P2 c1’ c1’’ c2’ c2’’ a11 a12 a21 a22 167 200 54 66 1,2 0,3 1,5 0,3 4 4 7 8
Предлагаю перенести данную консультацию в раздел "Исследование операций". Если перенесёте, то не забудьте, пожалуйста, сообщить об этом всем экспертам того раздела.
Здравствуйте, может у кого-то есть возможность проверить всю контрольную по данному предмету, там три задачи, просто сомневаюсь в правильности. спасибо, заранее за ответ.
Я предлагаю Вам сверить математическую модель задачи, построенную мной, с моделью, построенной Вами. У меня получилось так:
при условии, что
Но это не задача нелинейного программирования. Что получилось у Вас?
Возможно, я неправильно понял условие задачи, полагая, что имеется в виду себестоимость производства всего объёма продукции. Если имеется в виду себестоимость производства единицы продукции, то целевая функция будет такой:
Действительно, математическая модель задачи такова:
при условии, что
Я исправил ошибку, допущенную мной в сообщении на мини-форуме консультации. Указанное мной выражение для целевой функции получается из того, которое привели Вы в своём решении, после раскрытия скобок и приведения подобных членов.
Просмотрев решение, выполненное Вами в MS Excel, я считаю его ход правильным. К сожалению, в моём распоряжении теперь нет версии MS Excel с полным набором опций, поэтому я не могу проверить полученный Вами результат.
Спасибо вам огромное)))На протяжении уже трех лет вы мне помогаете в учебе на заочном отделении, принцип нашего вуза : "Сначала выучи сам, а потом мы расскажем, как это делается",- так и учусь)) Иду на красный диплом, поэтому переживаю за выполненные мной контрольные) Еще раз, СПАСИБО)
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Гордиенко Андрей Владимирович 