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Консультация № 194144
09.12.2018, 12:07
0.00 руб.
09.12.2018, 13:55
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2
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Здравствуйте! Прошу помощи в следующем вопросе:
Функции спроса и предложения имеют соответственно вид:
D(p)=100x-4p;S(p)=40x+x^2 p
где p – цена товара (услуги), x – некоторый технологический параметр. Равновесная цена определяется равенством спроса и предложения. Найти положительное значение величины x, при котором равновесная цена будет наибольшей, если 1≤x≤5. Найти наибольшее значение равновесной цены.
Решение.
D(p)=S(p)
100x-4p=40x+x^2 p
100x-4p-40x-x^2 p=0
x^2 p-60x+4p=0
При x=1
1^2*p-60*1+4p=0
5p=60
p=60/5
p=12
При x=5
5^2*p-60*5+4p=0
25p-300+4p=0
29p=300
p=300/29
p≈10.34
При x=1 равновесная цена наибольшая и равна p=12.
Вычисляем первую производную
(x^2 p-60x+4p)^'=2xp-60+4p
Находим критические точки, т.е. приравниваем производную к нулю:
2xp-60+4p=0; (2x+4)p-60=0;p=60/(2x+4)
Или я что-то неправильно делаю, подскажите пожалуйста
Функции спроса и предложения имеют соответственно вид:
D(p)=100x-4p;S(p)=40x+x^2 p
где p – цена товара (услуги), x – некоторый технологический параметр. Равновесная цена определяется равенством спроса и предложения. Найти положительное значение величины x, при котором равновесная цена будет наибольшей, если 1≤x≤5. Найти наибольшее значение равновесной цены.
Решение.
D(p)=S(p)
100x-4p=40x+x^2 p
100x-4p-40x-x^2 p=0
x^2 p-60x+4p=0
При x=1
1^2*p-60*1+4p=0
5p=60
p=60/5
p=12
При x=5
5^2*p-60*5+4p=0
25p-300+4p=0
29p=300
p=300/29
p≈10.34
При x=1 равновесная цена наибольшая и равна p=12.
Вычисляем первую производную
(x^2 p-60x+4p)^'=2xp-60+4p
Находим критические точки, т.е. приравниваем производную к нулю:
2xp-60+4p=0; (2x+4)p-60=0;p=60/(2x+4)
Или я что-то неправильно делаю, подскажите пожалуйста
Обсуждение
09.12.2018, 13:58
общий
Обратите внимание на данную консультацию, перенесённую из другого раздела.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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