can someone please solve this: a university is trying to determine what price to charge for tickets to football games. at a price of 30$ per ticket, attendance averages 40000 people per game. every decrease of $2 adds 10000 people to the average number. every person at the game spends an average of $6.00 on concessions. what price should be charged in order to maximize revenue?

Question

anonymous · Answer

What course is this for? You can solve using calculus....

anonymous · Answer

ap calc, but i don't understand it. could you solve it?

anonymous · Answer

No, but I can help you solve it.

anonymous · Answer

First thing you need to do is come up with a formula to optimize.

anonymous · Answer

i tried that, looking up how to do it online, but my online assignment is due in a few minutes so i need to hurry up :/ i've gotten it to a point, hold on (:

anonymous · Answer

Revenue = #people * cost of ticket + #people * $6

anonymous · Answer

Every decrease of $2 adds 10,000 people or
Every decrease of $1 adds 5000 people

anonymous · Answer

40000+(10000/2)x

anonymous · Answer

Revenue = (40,000 + 2,500 x) (30 - x) + 6 (40,000 + 2500 x)

anonymous · Answer

Simplify.

anonymous · Answer

We know that f(x) is maximized at x when f'(x) = 0 and f''(x) < 0

anonymous · Answer

to simplify would i foil the first two then distribute the 6 to the right side and add them together?

anonymous · Answer

yes. Should get a second degree polynomial.

anonymous · Answer

Take the derivative, set equal to 0.