The Summer Theatre charges $10 per ticket and it has had a full house of 500 nightly. The manager estimates that the ticket sales would decrease by 50 for each $2 increase in ticket cost. What is the most profitable price to charge for each ticket? At this new price what is the maximum revenue the Summer Theater can expect to generate?
When you say sales would decrease by 50, does that mean the actual sales, or the number of tickets? I'll assume the latter, or things would get tricky.
If there are x price increases, then revenue is price * quantity:
(10+2x)(500-50x)
The vertex of this parabola is at (5/2,5625)
Hmmm. How do you have 5/2 price increases?