CASE STUDY CHALLENGE

Optimization: Magazine Revenue Analysis

A magazine company circulates its magazine on a monthly basis in a city. It has 10,000 readers on its list and collects fixed charges of ₹ 4,000 per reader annually.

The company proposes to increase the annual subscription, but on the basis of a survey result, it predicted that for every increase of ₹ 5, ten readers will discontinue the service of this magazine company.

Based on the above information, answer the following questions:

Answer the following:

(i) Let the company increase ₹ x, then find the function R(x) representing the earnings of the company. [1]
(ii) Find d/dx (R(x)). [1]
(iii) (a) What subscription increase will bring maximum earnings for the company?

— OR —

(b) What will be the maximum value of R(x)?

[2]