This is a grade 11 math problem (20-1) in need of urgent help

Question

Starlights Productions is hosting an annual outdoor concert. Average attendance is 30000 people when tickets are $200. For every $5 increase in ticket price, 500 fewer people are expected to attend the concert.

a. Write a quadratic function in standard form that represents the revenue earned. Be sure to indicate what the variables represent.

b. What admission price will produce the most revenue? Explain how this can be determined.

c. How many people will attend if the maximum revenue is attained?

Answer 1

Let x = number of $5 increases

R(x) = revenue for x $5 increases = (number of tickets sold)(Price per ticket) = (30000 - 500x)(200 + 5x)

The graph of y = R(x) is a parabola opening downward. The x-intercepts are 60 and -40.

The maximum revenue occurs halfway between the x-intercepts.

So, maximum revenue when x = 10.In other words, to maximize revenue, the price should be increased 10 times by $5 each time. So, the optimal price would be 200 + 5(10) = $250.

Maximum Revenue = R(10) = (25000)(250) = $6,250,000