You have just opened a new dance club, Swing Haven, but are unsure of how high to set the cover charge (entrance fee). One week you charged $4 per guest and averaged 80 guests per night. The next week you charged $9 per guest and averaged 45 guests per night. (a) Find a linear demand equation showing the number of guests q per night as a function of the cover charge p. q(p) = (b) Find the nightly revenue R as a function of the cover charge p. R(p) = (c) When you set the admission top dollars, the club's nightly costs, including rent, salaries, and two free non-alcoholic drinks for each guest, amounts to C(p) =-27p +547 Find the profit in terms of the cover charge p. P(p) = (d) Determine entrance fees that allow Swing Haven to break even. Enter the lower fee first, and round your answer to two decimal places. When the entrance fee is p = or dollars per guest, then Swing Haven breaks even.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.3: Lines
Problem 92E
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You have just opened a new dance club, Swing Haven, but are unsure of how high to set the cover charge (entrance fee). One week
you charged $4 per guest and averaged 80 guests per night. The next week you charged $9 per guest and averaged 45 guests per
night.
(a) Find a linear demand equation showing the number of guests q per night as a function of the cover charge p.
q(p) =
(b) Find the nightly revenue R as a function of the cover charge p.
R(p) =
(c) When you set the admission top dollars, the club's nightly costs, including rent, salaries, and two free non-alcoholic drinks
for each guest, amounts to
C(p) =-27p +547
Find the profit in terms of the cover charge p.
P(p) =
(d) Determine entrance fees that allow Swing Haven to break even. Enter the lower fee first, and round your answer to two
decimal places.
When the entrance fee is p =
or
dollars per guest, then Swing Haven breaks even.
Transcribed Image Text:You have just opened a new dance club, Swing Haven, but are unsure of how high to set the cover charge (entrance fee). One week you charged $4 per guest and averaged 80 guests per night. The next week you charged $9 per guest and averaged 45 guests per night. (a) Find a linear demand equation showing the number of guests q per night as a function of the cover charge p. q(p) = (b) Find the nightly revenue R as a function of the cover charge p. R(p) = (c) When you set the admission top dollars, the club's nightly costs, including rent, salaries, and two free non-alcoholic drinks for each guest, amounts to C(p) =-27p +547 Find the profit in terms of the cover charge p. P(p) = (d) Determine entrance fees that allow Swing Haven to break even. Enter the lower fee first, and round your answer to two decimal places. When the entrance fee is p = or dollars per guest, then Swing Haven breaks even.
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