A telephone company in a town has 500 subscribers on its list and collects fixed charges of Rs 300/- per subscriber per year. The company proposes to increase the annual subscription and it is believed that for every increase of Rs 1/- one subscriber will discontinue the service. Find what increase will bring maximum profit?
Let’s consider that the company increases the annual subscription by Rs x.
So, x is the number of subscribers who discontinue the services.
Total revenue, R(x) = (500 – x) (300 + x)
= 150000 + 500x – 300x – x2
= -x2 + 200x + 150000
Differentiating both sides w.r.t. x, we get R’(x) = -2x + 200
For local maxima and local minima, R’(x) = 0
-2x + 200 = 0 ⇒ x = 100
R’’(x) = -2 < 0 Maxima
So, R(x) is maximum at x = 100
Therefore, in order to get maximum profit, the company should increase its annual subscription by Rs 100.
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