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 $10 per guest and averaged 300 guests per night. The next week you charged $15 per guest and averaged 250 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.
b. Find the nightly revenue R as a function of the cover charge p.
c. The club will provide two free nonalcoholic drinks for each guest, costing the club $3 per head. In addition, the nightly overheads (rent, salaries, dancers, DJ, etc.) amount to $3,000. Find the cost C as a function of the cover charge p.
d. Now find the profit in terms of the cover charge p, and hence determine the entrance fee you should charge for a maximum profit.
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