For an outdoor concert, a ticket price of $30 typically attracts 5000 people. For each $1 increase in the ticket price, 100 fewer people will attend. The revenue, R, is the product of the number of people attending and the price per ticket.

Question

a) Let x represent the number of $1 price increases. Find an equation expressing the total revenue in terms of x.
b) State any restrictions on x. Can x be a negative number? Explain.
c) Find the ticket price that maximizes
revenue.

I have already got a and b. I only need help in c).

Answer 1

I hope your function looks something like this:

R(x) = (5000 - 100x)(30 + x)
= 150000+ 5000x - 3000x - 100x^2
= -100x^2 + 2000x + 150000

this is a standard parabola opening dowwards , so it will have a maximum
the x of the vertex is -b/(2a) = -2000/-200 = 10

So there should be 10 increases of $1, each ticket costing $40.

number of tickets sold = 4000
cost of ticket = 40
revenue = 40(4000) = 160000

Answer 2

thx!