A magazine seller has 500 subscribers and collects annual subscription charges of Rs.300 per
subscriber. She proposes to increase the annual subscription charges and it is believed that for
every increase of Re 1, one subscriber will discontinue. What increase will bring maximum
income to her? Make appropriate assumptions in order to apply derivatives to reach the
solution. Write one important role of magazines in our lives.
Answers
Answer+100rupees per subscription
Given : A magazine seller has 500 subscribers and collects annual subscription charges of Rs.300 per subscriber.
every increase of Re 1, one subscriber will discontinue.
To Find : What increase will bring maximum income to her
Solution:
Subscribers = 500
Charges = 300
Charge increased = x then subscriber left = x
Revenue R = ( 300 + x)(500 - x)
dR/dx = (300 + x) (-1) + (1)(500 - x)
= -300 - x + 500 - x
=200 - 2x
dR/dx = 0
=> 200 - 2x = 0
=> x = 100
d²R/dx² = - 2 <0
Hence maximum revenue at x = 100
Max revenue = (300 + 100)(500 - 100) = 16000
Increasing price by 100 will will bring maximum
income to her
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