SOLUTION: A new movie theater holds 300 people. They found that when the price was $5 per ticket, the average sales would be 270 people per show. Each time they increase the price by $1, the

1.  Let N(x) be this function: the number of viewers at the ticket price of x dollars.

    Then N(x) = 270 - 15(x-5).    (1)

    It is exact translation of this statement: "Each time they increase the price by $1, the average attendance drops by 15 people."

    So, the question A) is answered, and the answer is: the attendance is 

        N(x) = 270 - 15(x-5) = 345 - 15x.

    where x is the ticket price in dollars.


2.  The revenue R(x) is   R(x) = N(x)*x = x*(345 - 15x) = .     (2)

    See the plot below.   So, the question B) is answered, too.


3.  The maximum of the quadratic function (2) is achieved at x =  =  = 11.5.


     Thus the optimum price is 11.5 dollars per ticket.
     The attendance then is N(11.5) = 270 - 15*(11.5-5) = 172.5 persons. 





        Plot y =