SOLUTION: A company can sell 2000 magazine subscriptions at $40 each. For each $5 increase in the price, it will sell 200 fewer subscriptions. What subscription price will provide the maximu

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A company can sell 2000 magazine subscriptions at $40 each. For each $5 increase in the price, it will sell 200 fewer subscriptions. What subscription price will provide the maximu      Log On


   

Question 1127464: A company can sell 2000 magazine subscriptions at $40 each. For each $5 increase in the price, it will sell 200 fewer subscriptions. What subscription price will provide the maximum revenue for the company?
Answer by josgarithmetic(39629) About Me  (Show Source):
You can put this solution on YOUR website!
That also means, for every 1 dollar price increase, 200%2F5 fewer subscriptions. 
PRICE         HOW MANY SUBSCRIPTIONS
40              2000
400+d          2000-(200/5)d

for d number of dollars

Revenue, %2840%2Bd%29%282000-%28200%2F5%29d%29.
You want to find the maximum of this revenue and the corresponding d number of dollars to add or subtract for this maximum d.

40%2840%2Bd%29%2850-d%29
zeros at d of -40, and +50.

%28-40%2B50%29%2F2=10%2F2=highlight_green%285%29


This means, best revenue is for 40%2B5=highlight%2845%29 dollars.
This max revenue, 40%2A45%2A45=highlight%2881000%29