Question Solved1 Answer 5. (-/5 Points] DETAILS WANEFMACZ 2.1.041 MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 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 $6 per guest and averaged 240 guests per night. The next week you charged $8 per guest and averaged 220 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. op) = (b) Find the nightly revenue R as a function of the cover charge p. RP) = (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() = (d) Now find the profit in terms of the cover charge p. PP) = Determine the entrance fee you should charge for a maximum profit (in dollars). p = $ per quest Need Help? Read it

CZ17LS The Asker · Algebra

Transcribed Image Text: 5. (-/5 Points] DETAILS WANEFMACZ 2.1.041 MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 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 $6 per guest and averaged 240 guests per night. The next week you charged $8 per guest and averaged 220 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. op) = (b) Find the nightly revenue R as a function of the cover charge p. RP) = (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() = (d) Now find the profit in terms of the cover charge p. PP) = Determine the entrance fee you should charge for a maximum profit (in dollars). p = $ per quest Need Help? Read it
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Transcribed Image Text: 5. (-/5 Points] DETAILS WANEFMACZ 2.1.041 MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 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 $6 per guest and averaged 240 guests per night. The next week you charged $8 per guest and averaged 220 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. op) = (b) Find the nightly revenue R as a function of the cover charge p. RP) = (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() = (d) Now find the profit in terms of the cover charge p. PP) = Determine the entrance fee you should charge for a maximum profit (in dollars). p = $ per quest Need Help? Read it
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Solution :Given point (p_(1)q_(1))=(6,240){:[(p_(2),q_(2))=(8","220)],[=>q+q_(1)=(Delta q)/(Delta p)*(p-p_(1))],[q-240=(-20)/(2)(p-6)],[q-240=-10 p+60],[qq=300-10 p],[" Demand function "q(p)=300-10 p]:}(b){:[" Revenue "=p*q=p(300-10 p)],[R(p)=300 p-10p ... See the full answer