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You have just opened a new nightclub, Russ' Techno Pitstop, but are unsure of how high to set the cover charge (entrance fee). One week you charged $9 per guest and averaged 320 guests per night. The next week you charged $11 per guest and averaged 280 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) The club will provide two free non-alcoholic drinks for each guest, costing the club $3 per head. In addition, the nightly overheads (rent, salaries, dancers, DJ, etc.) amount to $1,000. Find the cost C as a function of the cover charge p. C(p) =     (d) Now find the profit in terms of the cover charge p. P(p) =     Determine the entrance fee you should charge for a maximum profit.p = $ per guest

You have just opened a new nightclub, Russ' Techno Pitstop, but are unsure of how high to set the cover charge (entrance fee). One week you charged $9 per guest and averaged 320 guests per night. The next week you charged $11 per guest and averaged 280 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) The club will provide two free non-alcoholic drinks for each guest, costing the club $3 per head. In addition, the nightly overheads (rent, salaries, dancers, DJ, etc.) amount to $1,000. Find the cost C as a function of the cover charge p. C(p) =     (d) Now find the profit in terms of the cover charge p. P(p) =     Determine the entrance fee you should charge for a maximum profit.p = $ per guest

College Algebra
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 nightclub, Russ' Techno Pitstop, but are unsure of how high to set the cover charge (entrance fee). One week you charged $9 per guest and averaged 320 guests per night. The next week you charged $11 per guest and averaged 280 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) The club will provide two free non-alcoholic drinks for each guest, costing the club $3 per head. In addition, the nightly overheads (rent, salaries, dancers, DJ, etc.) amount to $1,000. Find the cost C as a function of the cover charge p.
C(p) =
 
 

(d) Now find the profit in terms of the cover charge p.
P(p) =
 
 

Determine the entrance fee you should charge for a maximum profit.
p = $ per guest
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