Question

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 Rs 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.

Answer 1

Let the seller increases Rs x in annual subscription.

$\therefore$ Total revenue generated by her, $R\left(x\right)=Rs(300+x)(500-x)$

Diff. w.r.t. x both sides, $R^{\prime }\left(x\right)=-(300+x)+(500-x)=200-2x$

Again diff. w.r.t. $x,R"\left(x\right)=-2$

For the points of local maxima & local minima, $R^{\prime }\left(x\right)=0\Rightarrow x=100$

Now, $R"(x=100)=-2<0\therefore R\left(x\right)$ is maximum at $x=100.$

So, an increment of Rs 100 will maximize the profit.
Important role of magazines in our lives : Magazines contribute a great deal, to the development of our knowledge. Through valuable and subtle critical and commentrary articles on culture, social civilization, new life style we learn a lot of interesting things. Through reading magazines, our mind and point of view are consolidated and enriched.