Question

АНтон является владельцем двух заводов в разных городах.на заводе производятся абсолютно одинаковые товары при использовании разных технологий.если рабочие на одном из заводов трудятся суммарно t^2 часов в неделю,то производят t единиц товара.За каждый час работы Антон платит рабочему на первом заводе 250 рублей,а на втором 200 рублей.Антон готов выделять 900000 тысяч рублей в неделю на оплату труда рабочих.Какое наименьшее количество единиц товара можно произвести на этих двух заводах?

Answer 1

x² часов трудятся на I заводе.

y² часов трудятся на II заводе.

x товаров производят на I заводе.

y товаров производят на II заводе.

Час на I заводе = 250 руб.

Час на II заводе = 200 руб.

Затраты на оплату = 9*10⁵ руб.

s=x+y, s - суммарное производство.

Найти $s_{max}$

Составим систему уравнений:

$\left \{ {{s=x+y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \atop {250x^{2}+200y^{2}=9*10^{5}}} \right.$

Выразим одно через другое:

$\left \{ {{x=s-y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \atop {250(s-y)^{2}+200y^{2}=9*10^{5}}} \right$

$></p><p>Сокращаем, открываем скобки:</p><p><img src=$

$D=162*10^{3}-20s^{2}$

$></p><p>s ∈ (-∞;90]</p><p><img src=$

Ответ: 90 - наибольшее количество единиц товара, которое можно произвести на этих двух заводах.

Answer 2

                   Решение : //////////////////////////////

Answer 3

Problem Analysis

We have two factories owned by Anton, located in different cities. Both factories produce identical goods but use different technologies. The number of units produced is directly proportional to the total hours worked in one of the factories. Anton pays the workers at the first factory 250 rubles per hour and at the second factory 200 rubles per hour. Anton has a budget of 900,000 rubles per week for labor costs. We need to determine the minimum number of units that can be produced in these two factories.

Solution

Let's assume the number of hours worked in the first factory is t^2. According to the problem statement, this will result in t units of goods produced.

To find the minimum number of units produced, we need to maximize the number of hours worked in the first factory while staying within the budget of 900,000 rubles.

Let's calculate the maximum number of hours that can be worked in the first factory:

1. The cost per hour at the first factory is 250 rubles. 2. The total budget for labor costs is 900,000 rubles per week. 3. Therefore, the maximum number of hours worked in the first factory is 900,000 / 250 = 3600 hours per week.

Now, let's calculate the corresponding number of units produced in the first factory:

1. The number of units produced is directly proportional to the number of hours worked. 2. If t^2 hours result in t units, then 3600 hours will result in sqrt(3600) units.

Using the formula for the square root, we can calculate the number of units produced in the first factory:

Number of units produced in the first factory = sqrt(3600) = 60 units

Since the factories produce identical goods, the number of units produced in the second factory will also be 60 units.

Therefore, the minimum number of units that can be produced in these two factories is 60 units.

Conclusion

The minimum number of units that can be produced in Anton's two factories, given the budget of 900,000 rubles per week and the different payment rates for the workers, is 60 units.