The park had initially planned to charge $8 for admission and expected to have 2400 visitors a day. Allison and Juan were assigned the task of analyzing the park's admission revenues.

Question

1.a)How much revenue would the park have for one day at the current price?

b)They have been provided with some market research that shows for every $0.50 the admission price is raised, the park will have 80 fewer visitors. How much would the park revenue be if park raised their admission price by $1?

c)After a few calculations, Allison and Hannah realize the park will make more money if they raise the price of admission. However, they also understand that there must be a limit to how much the park can charge. As a result, they model the situation with the equation, R = (2400 - 80x)(8 + 0.5x), where R represents the revenue from sales and x represents the number of price increases.

i)Write this equation in standard form, R = ax2 + bx + c. Show all of the steps leading to the final answer.

ii)What price should the park charge to maximize its revenue?

iii)What price range would produce a revenue over $20,000?

Answer 1

just remember that revenue = price * no.tickets.sold

You can use that to answer all these questions.

Give it a try, and come back if you get stuck.

also, recall that the vertex of a parabola ax^2+bx+c is at x = -b/2a. For R(x), that is where the maximum revenue occurs.