You have just opened a new night CLUB, Russ' Techno Pit stop, but are unsure how high to set the cover charge.
One week, you charge $ 10 per guest and averaged 300 guests per night. The next week you charged $ 15 per guest and averaged 250 guest per night.
Find a linear demand equation showing the number of guests q per night as a function of the cover charge p.
Find the nightly revenue R as a function of the cover charge p The club will provide 2 free non-alcoholic drinks for each guest, costing the club $3 per head. In addition, the nightly overhead (rent, salaries, DJ, etc) amount to $3000.
Find the cost C as a function of the cover charge p. Now, find the profit in terms of the cover charge p, and hence determine the cover charge you should charge for a maximum profit.