Question

A telephone company in the town has 5000 subscribers on its list and collects fixed rent charges of Rs. 3000 per year from each person. The company proposes to increase annual rent and it is believed that for every increase of 1 rupee in the rent one subscriber will be discontinued. Find what increased annual rental will bring the maximum annual income to the company.

Answer 1

company income per year =5000*3000
=15000000
company income after increase of Rs1
=5000*3001=15005000

Answer 2

Answer:

Rs 1000 Annual increase will bring maximum profit

Step-by-step explanation:

Total Subscribers = 5000

Rental per year from a subscriber = Rs 3000

Total Rent received = 5000 * 3000 = Rs 15 * 10⁶

Subscriber + Rent = 5000 + 3000 = 8000

For every increase in Rent One Subscriber will be reduced .

Let say X Rental increased then X subscribers decreased

Total Rent received = (5000 -X)(3000 + X)

5000 - X + 3000 + X = 8000

Max value  of product is at center 8000/2 = 4000

5000 - X = 4000

=> X = 1000

Maximum Rent Received = 4000 * 4000 =  Rs 16 * 10⁶

Rs 1000 Annual increase will bring maximum profit

Other Method

f(x) =  (5000 -X)(3000 + X)

=> f(x) = -X² + 2000X  + 15×10⁶

df(x)/dx = -2X + 2000

To get max value

df(x)/dx = 0

-2X + 2000 = 0

=> X = 1000