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Консультация № 190446
17.01.2017, 19:31
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Определить наружные размеры открытого прямоугольного ящика с заданной толщиной стенок d и емкостью V так, чтобы на его изготовление было затрачено наименьшее количество материала.
Спасибо!
Определить наружные размеры открытого прямоугольного ящика с заданной толщиной стенок d и емкостью V так, чтобы на его изготовление было затрачено наименьшее количество материала.
Спасибо!
Обсуждение
18.01.2017, 10:37
общий
это ответ
Здравствуйте, Анна Витальевна!
По-моему, задачу можно решить так. Обозначим внутренние длину, ширину и высоту ящика соответственно буквами
При этом выполняется соотношение 
откуда 
При плотности 
материала стенок ящика и толщине 
на изготовление ящика потребуется масса 
материала, равная
Вычислим экстремум функции
в соответствии с необходимыми условия экстремума,
Следовательно, наружные длина, ширина и высота ящика соответственно равны
Разумеется, нужно убедиться в том, что при вычисленных значениях
функция 
достигает минимума. Я надеюсь, что Вы сможете сделать это сами. Заодно проверите и правильность предложенного решения задачи.
По-моему, задачу можно решить так. Обозначим внутренние длину, ширину и высоту ящика соответственно буквами
При этом выполняется соотношение откуда При плотности материала стенок ящика и толщине на изготовление ящика потребуется масса материала, равнаяВычислим экстремум функции
в соответствии с необходимыми условия экстремума,
Следовательно, наружные длина, ширина и высота ящика соответственно равны
Разумеется, нужно убедиться в том, что при вычисленных значениях
функция достигает минимума. Я надеюсь, что Вы сможете сделать это сами. Заодно проверите и правильность предложенного решения задачи.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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