A private telephone company serving a small community makes a profit of Rs. 12.00 per subscriber, if it has 725 subscribers. It decides to reduce the rate by a fixed sum for each subscriber over 725 , thereby reducing the profit by one paise per subscriber. Thus there will be profit of Rs. 11.99 on each the 726 subscriber, Rs. 11.98 on each of 727 subscribers etc. What is the number of subscribers which will give the company the maximum profit?

Question

A private telephone company serving a small community makes a profit of Rs. 12.00 per subscriber, if it has 725 subscribers. It decides to reduce the rate by a fixed sum for each subscriber over 725 , thereby reducing the profit by one paise per subscriber. Thus there will be profit of Rs. 11.99 on each the 726 subscriber, Rs. 11.98 on each of 727 subscribers etc. What is the number of subscribers which will give the company the maximum profit? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Let no. of subscriber increased by x. Hence profit now subscriber =12-(x/100)[. REE . prime 90,6] ∴ Total profit = P ( x )=( x +725)(12-( x /100)) P prime(x)=0 gives x=237.5 ; no. of subscriber =725+237 or 725+238

Let no. of subscriber increased by x. Hence profit now subscriber =12−100x​[ REE ′90,6] ∴ Total profit =P(x)=(x+725)(12−100x​) P′(x)=0 gives x=237.5; no. of subscriber =725+237 or 725+238

Let no. of subscriber increased by $x$ . Hence profit now subscriber $= 12 - \frac{x}{100} [$ REE $^{'} 90, 6]$
$∴$ Total profit $= P (x) = (x + 725) (12 - \frac{x}{100})$
$P^{'} (x) = 0$ gives $x = 237.5;$ no. of subscriber $= 725 + 237$ or $725 + 238$