Calculus
posted by Sydney .
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 165 guests per night. The next week you charged $10 per guest and averaged 150 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 nonalcoholic 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.
p = $ per guest.
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