The money to be spent for the welfare of the employees of a firm

Question:

The money to be spent for the welfare 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) recieved from the sale of $x$ units of a product is given by $R(x)=3 x^{2}+36 x+5$, find the marginal revenue, when $x=5$, and write which value does the question indicate.

Solution:

Since, marginal revenue is the rate of change of total revenue with respect to the number of units sold, we have

Marginal revenue $(\mathrm{MR})=\frac{\mathrm{d} R}{\mathrm{~d} x}=6 x+36$

When $x=5, \mathrm{MR}=6(5)+36=66$

Hence, the required marginal revenue is ₹66.

It indicates the extra money spent when number of employees increased from 5 to 6.

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