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Консультация № 183314
24.05.2011, 16:40
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
1) функция издержек имеет вид С(х)=40х+0,08х^3. цена реализации единицы продукции равна 200 ден. ед. Найти, при каком объеме выпускаемой продукции полученная прибыль является эластичной.
2) монополия производит фиксированное количество х единиц товара и устанавливает на единицу товара цену р>р0. количество реализованного товара К зависит от р (р0-цена, при которой будет реализован весь товар). определить значение р, при котором монополия получит максимальную прибыль. найти допустимые значения р0. К(р)=хе^(р0-р)
1) функция издержек имеет вид С(х)=40х+0,08х^3. цена реализации единицы продукции равна 200 ден. ед. Найти, при каком объеме выпускаемой продукции полученная прибыль является эластичной.
2) монополия производит фиксированное количество х единиц товара и устанавливает на единицу товара цену р>р0. количество реализованного товара К зависит от р (р0-цена, при которой будет реализован весь товар). определить значение р, при котором монополия получит максимальную прибыль. найти допустимые значения р0. К(р)=хе^(р0-р)
Обсуждение
24.05.2011, 17:43
общий
это ответ
Здравствуйте, Лаптев Александр Владимирович!
Ответ на первый вопрос.
Прибыль PI=R(x)-C(x)=200*x-(40*x+0.08*x3)=160*x-0.08*x3
Дифференцируем по x и приравниваем нулю
160-0.24*x2=0
По смыслу задачи, x - неотрицательна
x=[$8730$](160/0.24)=25,8 шт. = 26 шт.
Тогда максимальная прибыль MaxPi=160*26-0.08*263=4160-1406,1=2753,9 ден ед.
Удачи!
Ответ на первый вопрос.
Прибыль PI=R(x)-C(x)=200*x-(40*x+0.08*x3)=160*x-0.08*x3
Дифференцируем по x и приравниваем нулю
160-0.24*x2=0
По смыслу задачи, x - неотрицательна
x=[$8730$](160/0.24)=25,8 шт. = 26 шт.
Тогда максимальная прибыль MaxPi=160*26-0.08*263=4160-1406,1=2753,9 ден ед.
Удачи!
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