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 1 paise per subscriber. Thus, there will be profit of Rs. 11.99 on each of the 726 subscribers, Rs. 11.98 on each of the 727 subscribers, etc. What is the number of subscribers which will give the company the maximum profit?

Answer

962 or 963

Explanation

Let the addtion number of subscrberes be x .So the number of subscribers becomes 725 + x and then the profit per subscriber is Rs `(12-x//100)`
If p is the total profit in rupee then
`P=(725+x)(12-(x)/(1000))`
`=1/100[870000+(475)/(2)^(2)-(x-(475)/(2))^(2)]`
P is maximum (greatest) when `x-475//2 =0 i.e x=237.5` But x is + ve integer so x can be taken as 237 or 238
Since P(237)=P(238) for maximum profit total number of subscriber should 725+237=962 or 725 + 238 =963