The current ticket price at a local theatre is $4, and the theatre attracts an average of 250 customers per show. every $.20 increase in ticket price reduces average attendance by 10 customers, while every $.20 decrease results in 10 extra customers.
a) let x respresent the change in ticket price. show that revenue R from ticket sales depends of x according to .
I differentiated this and solved for x and found x=1/2 and because the rate of change is not zero the sales depend on the value of x. Correct?
b) if the seating capacity is 400, show that
I'm not sure what to do, I rewrote the function as but I just ended up with a x value of 10 when I differentiated.
c) find the ticket price that will maximize revenue.
so I wrote
then I differentiated and came to a value of x = 2.5
then solve R(x) for x = -3, x = 2.5, x=5 and found the optimum price at x=2.5 for a price of $4.50
solving gave me the same result but x = -2.5
Are A and C correct, and what am I doing incorrectly for B?