Nightclub Management 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 $5 per guest and averaged 225 guests per night. The next week you charged $12 per guest and averaged 120 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) =
Nightclub Management 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 $5 per guest and averaged 225 guests per night. The next week you charged $12 per guest and averaged 120 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) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Nightclub Management 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 $5 per guest and averaged 225 guests per night. The next week you charged $12 per guest and averaged 120 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 $2 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 (in dollars).
p = $ per guest
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