SOLUTION: A certain band charges $51 per ticket for concerts when 1694 people attend. The band members realize that for every $3 increase in the ticket price 22 fewer people will attend the

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Question 1099679: A certain band charges $51 per ticket for concerts when 1694 people attend. The band members realize that for every $3 increase in the ticket price 22 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.
1.) R(x)=
2.) What should the ticket price be for the band to maximize its revenue? $
3.) How many people will attend the concert when the revenue is maximized?
4.) What is the band's maximum revenue? $


I'm having trouble figuring out this problem, any help is much appreciated! Thank you!

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A certain band charges $51 per ticket for concerts when 1694 people attend.
The band members realize that for every $3 increase in the ticket price 22 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.
:
Let X = no. of $3 increases and no. of 22 ticket decreases
1.) R(x)= (1694-22x)*(51+3X)
FOIL
R(x) = 86394 + 5082x - 1122x - 66x^2
R(x) = -66x^2 + 3960x + 86394 is the revenue function
:
2.) What should the ticket price be for the band to maximize its revenue?
This is a quadratic equation, the maximum will occur on the axis of symmetry
Find this using x = -b/(2a)
x = %28-3960%29%2F%282%2A-66%29
x = +30 ea $3 price increases for max revenue, therefore
30($3) + $51 = $141 will be he ticket price for max revenue
:
3.) How many people will attend the concert when the revenue is maximized?
1694 - 30(22) = 1034 people will attend
:
4.) What is the band's maximum revenue? $
1034 * $141 = $145,794