Question about a HW problem. The Problem is in the description.

Question

a baseball team plays in a stadium that holds 55000 spectators. when the ticket price is $10.00, the average attendance is 27,000. Reaseach has shown that on average, when the ticket price goes down by $0.10, the attendance goes up by 300

Answer 1

Let x = number of $0.10 decreases

Average attendance = 27000 + 300x

Ticket price = 10 - 0.10x

Assuming that you want to adjust the ticket price to maximize revenue:

Revenue = R(x) = (27000 + 300x)(10 - 0.10x) = -30x² + 300x + 270000

The graph of R(x) is a parabola opening downward

Max when R'(x) = -60x + 300 = 0

So, maximum revenue when x = 5

To maximize revenue, decrease the ticket price by 5($0.10) = $0.50

Maximum revenue R(5) = $270,750