Question

The money to be spent for the walfare of the employees of a firm is proportional to the rate of change of its total revenue (marginal revenue). If the total revenue (in rupees) received from the sales of $x$ units of a product is given by $R\left(x\right)=3x^2+36x+5$, find the marginal revenue, when $x=5,$ and write which value does the question indicates.

Answer 1

If the Total Revenue is given by $f\left(x\right)$, the Marginal Revenue is the rate of change of total revenue and is nothing but the first order derivative of the function $\frac{df\left(x\right)}{dx}$

Total revenue = $R\left(x\right)=3x^2+36x+5$

Differentiating the equation R(x), we get

$\frac{dR\left(x\right)}{dx}=6x+36$

If x = 5, Marginal revenue = 6(5) + 36 = 66.

Therefore, the Marginal revenue = 66.

The concern over the welfare of the employees by the employer.