SOLUTION: A video rental service has 1100 subscribers, each of whom pays $12 per month. On the basis of a survey, the company believes that for each decrease of $0.20 in the monthly rate, it

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A video rental service has 1100 subscribers, each of whom pays $12 per month. On the basis of a survey, the company believes that for each decrease of $0.20 in the monthly rate, it      Log On


   

Question 1135477: A video rental service has 1100 subscribers, each of whom pays $12 per month. On the basis of a survey, the company believes that for each decrease of $0.20 in the monthly rate, it could obtain 50 additional subscribers. At what rate will the maximum revenue be obtained, and how many subscribers will there be at that rate?
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x=number of -$0.20 per +50 more subscribers
(1100+50x)(12-0.20x) has to be maximized. This is 13200+380x-10x^2 and the vertex x value is at -b/2a or 380/20 or 19
This would be 19*50 more subscribers or 2050 total
They would each pay $3.80 less or $8.20 per month
The revenue would be $16810 a month.
graph%28300%2C300%2C-5%2C25%2C-1000%2C20000%2C%281100%2B50x%29%2812-0.20x%29%29