Question

I know I asked this question but I still am getting the wrong answer.

A certain band charges $142 per ticket for concerts when 1918 people attend. The band members realize that for every $3 increase in the ticket price 21 fewer people will attend the concert. Find a revenue function R in terms of x where x represents the number of additional $3 increases in the ticket price.

What should the ticket price be for the band to maximize its revenue?
How many people will attend the concert when the revenue is maximized?

I got the function but I got the ticket price is 22 because that is the critical point of the function am I doing something wrong?

Answer 1

base revenue = 142 * 1918 = 272,356
new revenue R = (142 + 3 x)( 1918-21x)
dR/dx = (142 + 3 x)(-21) + ( 1918-21x)(3) = -2982 -3x + 5754 - 63 x
= 2772 - 66 x
dR/dx = 0 at max or min
x = 2772 / 66 = 42 increases
3 x = 126 amount of increase
142 + 126 = $ 268 per ticket
well, I did that fast but did not get 22

Answer 2

ok but when i enter 22 into the question it tells me that that is correct but it still is saying I'm getting the other 2 questions incorrect

Answer 3

(142 + 3 x)( 1918-21x) = -63x^2 + 2772x + 272356
the vertex occurs at x = -b/2a = 2772/126 = 22
1918-22*21 = 1456 people attended

Answer 4

oh, and x=22 means the ticket price is 142+3*22 = $208

Answer 5

ohhh got it thank you!!