1. a) You are not supposed to differentiate this. You are asked to GENERATE the equation you are given.
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?
okay is this correct then,
Total revenue is equal to the amount of customers times the price, if R is the revenue, p is equal the price, a is equal to the increase in price, q is equal to the amount of customers and b is to the amount of customers lost and x is equal to the amount of the number of times the price is increased. For every increase in x value there is a increase in price but a decrease in customers
R = (p+ax)(q-bx)
and when the price is 4+the increase times x, and the average customers is 250, and loss of customers is 50 times the value of x
R(x) = (4+x)(250-50x)
and so R(x) is dependent on x.
What about B and C?