A concert promoter finds she can sell 1000 tickets at $50 each. She will not sell the tickets for less than $50, but she finds that for every $1 increase in the ticket price above $50, she will sell 10 fewer tickets.
(a) Express n, the number of tickets sold, as a function of p, the price.
(b) Express R, the revenue, as a function of p, the price.
(c) Find the domain of the function found in part (b).
(d) Express R, the revenue, as a function of n, the number sold.
(e) Find the domain of the function found in part (d).
(f) Find the price that produces the maximum revenue.
(g) Find the number of tickets sold that produces the maximum revenue.
(h) Find the maximum revenue.
(i) Sketch the graph of the function found in part (b).
(j) Describe what the graph found in part (i) tells you about how the revenue varies with price.