Nightclub ManagementYou have justopened a new nightclub, Russ' TechnoPitstop, but are unsure of how high...

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Nightclub ManagementYou have justopened a new nightclub, Russ' TechnoPitstop, but are unsure of how high to set thecover charge (entrance fee). One week youcharged $8 per guest and averaged 240guests per night. The next week you charged$10 per guest and averaged 200 guests pernight.(a)Find a linear demand equation showing thenumber of guests q per night as a function ofthe cover charge p.q(p) =(b)Find the nightly revenue R as a function of thecover charge p.R(p) =(c)The club will provide two free non-alcoholicdrinks for each guest, costing the club $2 perhead. In addition, the nightly overheads (rent,salaries, dancers, DJ, etc.) amount to $1,000.Find the cost C as a function of the covercharge p.C(p) =(d)Now find the profit in terms of the covercharge p.P(p) =Determine the entrance fee you shouldcharge for a maximum profit (in dollars).p= $ per guest

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Nightclub ManagementYou have justopened a new nightclub, Russ' TechnoPitstop, but are unsure of how high to set thecover charge (entrance fee). One week youcharged $8 per guest and averaged 240guests per night. The next week you charged$10 per guest and averaged 200 guests pernight.(a)Find a linear demand equation showing thenumber of guests q per night as a function ofthe cover charge p.q(p) =(b)Find the nightly revenue R as a function of thecover charge p.R(p) =(c)The club will provide two free non-alcoholicdrinks for each guest, costing the club $2 perhead. In addition, the nightly overheads (rent,salaries, dancers, DJ, etc.) amount to $1,000.Find the cost C as a function of the covercharge p.C(p) =(d)Now find the profit in terms of the covercharge p.P(p) =Determine the entrance fee you shouldcharge for a maximum profit (in dollars).p= $ per guest