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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
A cable network provider in a small town has $500$ subscribers and he used to collect Rs. $300$ per month from each subscriber. He proposes to increase the monthly charges and it is believed that for every increase of Rs. $1$, one subscriber will discontinue the service.
The number of subscribers which gives the maximum revenue is:
Solution
From previous question,
Revenue:
$R=(300+x)(500-x)$
Expand:
$R=150000+200x-x^2$
This is a quadratic function:
$R=-x^2+200x+150000$
Maximum occurs at
$x=\frac{-b}{2a}$
Here,
$a=-1,; b=200$
$x=\frac{-200}{2(-1)}$
$x=100$
So number of subscribers:
$500-x=500-100=400$
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