Last year, a music theatre charged $60 admission, and at that price an average of 200 seats were sold for each show. A survey predicts that for every $5 increase in ticket price, 10 fewer people would be expected to attend the show.
a)write a quadratic function to model this situation.
b) how many seats would be empty when revenue is maximized compared to last year's average?
c) determine the admission price that would maximize revenue?
need this for practice for my upcoming quiz tomorrow. pls can u explain how did u get the two linear equation. i can change it to quadratic though, but i do not know how to set it up, thanks in advance guys :D.
a)write a quadratic function to model this situation.
b) how many seats would be empty when revenue is maximized compared to last year's average?
c) determine the admission price that would maximize revenue?
need this for practice for my upcoming quiz tomorrow. pls can u explain how did u get the two linear equation. i can change it to quadratic though, but i do not know how to set it up, thanks in advance guys :D.
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Revenue=(60+5x)(200-10x)
Expanded it becomes
R=12000+400x-50x^2
Axis of symmetry x=-(400)/(2*-50)
Axis of symmetry x=4
Ticket price 80 (60+5*4)
Tickets sold 160 (40 less than 200). The number of empty seats depends on the number of seats on the theater
Expanded it becomes
R=12000+400x-50x^2
Axis of symmetry x=-(400)/(2*-50)
Axis of symmetry x=4
Ticket price 80 (60+5*4)
Tickets sold 160 (40 less than 200). The number of empty seats depends on the number of seats on the theater
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thanks dude but ur kinda late hehe
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p = price
s = seat
s = ap + b
when p = 60, s = 200
when p = 65, s = 190
and so on
200 = 60a + b .... equation 1
190 = 65a + b .... equation 2
we get
a = -2
b = 320
so
s = -2p + 320
Revenue: R = s x p = (-2p+320) p = -2 p^2 + 320 p (answer a)
when maximized: R' = 0
R' = -4 p + 320
0 = -4 p + 320
4p = 320
p = 80
To maximize revenue, ticket price = $80 (answer c)
s = -2p + 320 = - 2 x 80 + 320 = 160
The seat taken is 160 seat. But I can't answer question b "how many seats would be empty" because it wasn't stated how many seat the theater had. 200 isn't
s = seat
s = ap + b
when p = 60, s = 200
when p = 65, s = 190
and so on
200 = 60a + b .... equation 1
190 = 65a + b .... equation 2
we get
a = -2
b = 320
so
s = -2p + 320
Revenue: R = s x p = (-2p+320) p = -2 p^2 + 320 p (answer a)
when maximized: R' = 0
R' = -4 p + 320
0 = -4 p + 320
4p = 320
p = 80
To maximize revenue, ticket price = $80 (answer c)
s = -2p + 320 = - 2 x 80 + 320 = 160
The seat taken is 160 seat. But I can't answer question b "how many seats would be empty" because it wasn't stated how many seat the theater had. 200 isn't