Question

Алгебра 11 Производная Предприятие получает от заказчика 150 руб. за погрузку в вагон 60 т груза. Предприятие платит грузчикам 60 руб., если они за час нагружают тонну груза. За каждый час простоя вагона под погрузкой предприятие платит штраф в размере 10 руб. При какой производительности труда грузчиков прибыль предприятия является наибольшей?

Answer 1

Пусть x  тонн в час - производительность труда грузчиков

$\frac{60}{x}$ часов -  время вагона под погрузкой.

$10\cdot \frac{60}{x} =\frac{600}{x}$   руб - расходы на оплату простоя вагона под погрузкой

Предприятие платит грузчикам 60 руб., если они за час нагружают тонну груза

Грузчики  нагружают за час  х тонн груза

60·х руб. - расходы на оплату труда грузчиков.

$S(x)=150-60x-\frac{600}{x}$  руб.  - прибыль должна быть положительной

Значит

$150-60x-\frac{600}{x}>0$

$5-2x-\frac{20}{x} >0$

$\frac{2x^2-5x+20}{x}$    ⇒   x <0  чего быть не может.

задача некорректна

Answer 2

Problem Analysis

To find the labor productivity that maximizes the company's profit, we need to determine the relationship between the labor productivity and the profit. We can then find the maximum point of this relationship.

Solution

Let's denote the labor productivity as x (in tons per hour). We can express the profit function P(x) as the difference between the revenue and the costs.

The revenue from loading the cargo is given by the product of the payment per ton and the amount of cargo loaded. In this case, the revenue function R(x) is given by:

R(x) = 150x

The costs consist of two components: the payment to the loaders and the penalty for each hour of wagon idle time. The cost function C(x) is given by:

C(x) = 60x + 10x

The profit function P(x) is the difference between the revenue and the costs:

P(x) = R(x) - C(x) = 150x - (60x + 10x) = 80x

To find the labor productivity that maximizes the profit, we need to find the value of x that maximizes P(x).

Maximizing the Profit

To find the maximum point of the profit function, we can take the derivative of P(x) with respect to x and set it equal to zero. Then, we solve for x.

Let's differentiate P(x) with respect to x:

P'(x) = 80

Setting P'(x) equal to zero:

80 = 0

Since the derivative is a constant, there is no critical point. Therefore, the profit function P(x) is always increasing, and there is no maximum point.

Conclusion

The profit of the company does not have a maximum point. Therefore, there is no specific labor productivity that maximizes the company's profit.

Please let me know if you need any further clarification.