Question Solved1 Answer The latest demand equation for your Yoda vs. Alien T-shirts is given by q = -40p + 500 where q is the number of shirts you can sell in one week if you charge $p per shirt. The Student Council charges you $300 per week for use of their facilities, and the T-shirts cost you $7 each. Find the weekly cost as a function of the unit price p. C(p) = -590x2 + Hence, find the weekly profit as a function of p. P(p) = Determine the unit price you should charge to obtain the largest possible weekly profit. p = $ per T-shirt What is the largest possible weekly profit? $ 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 200 guests per night. The next week you charged $15 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. – 20p 9(p) = 41 - (b) Find the nightly revenue R as a function of the cover charge p. R(p) = (c) The club will provide two free non-alcoholic drinks for each guest, costing the club $4 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

GVSX5B The Asker · Calculus

Transcribed Image Text: The latest demand equation for your Yoda vs. Alien T-shirts is given by q = -40p + 500 where q is the number of shirts you can sell in one week if you charge $p per shirt. The Student Council charges you $300 per week for use of their facilities, and the T-shirts cost you $7 each. Find the weekly cost as a function of the unit price p. C(p) = -590x2 + Hence, find the weekly profit as a function of p. P(p) = Determine the unit price you should charge to obtain the largest possible weekly profit. p = $ per T-shirt What is the largest possible weekly profit? $ 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 200 guests per night. The next week you charged $15 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. – 20p 9(p) = 41 - (b) Find the nightly revenue R as a function of the cover charge p. R(p) = (c) The club will provide two free non-alcoholic drinks for each guest, costing the club $4 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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Transcribed Image Text: The latest demand equation for your Yoda vs. Alien T-shirts is given by q = -40p + 500 where q is the number of shirts you can sell in one week if you charge $p per shirt. The Student Council charges you $300 per week for use of their facilities, and the T-shirts cost you $7 each. Find the weekly cost as a function of the unit price p. C(p) = -590x2 + Hence, find the weekly profit as a function of p. P(p) = Determine the unit price you should charge to obtain the largest possible weekly profit. p = $ per T-shirt What is the largest possible weekly profit? $ 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 200 guests per night. The next week you charged $15 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. – 20p 9(p) = 41 - (b) Find the nightly revenue R as a function of the cover charge p. R(p) = (c) The club will provide two free non-alcoholic drinks for each guest, costing the club $4 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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The latest demand equation for Yoda vs Alien T-shirts in giver by:q=-40 x+500Where q is number of shirtsfx is Charged price on per shirtEach T-shirt lost $7Ovir Aim is to determineweekly Cost functionWeekly profit functionCharge for maximum profitMaximum weekly profitTotal number. of shirt Sold per weekq=-40 x+500The cost of each shirt is $7other Lost =$300 charged bystudent louncil per week.Now,{:[" Total cost "=" Fixed cost "+" Variable lost "],[=$300+q($7)],[=$(300+7a_(1))]:}{:[=>],[" Total cost "=$(300+7(-40 x+500))],[=$(3800-280 x)],[=>C(x)=$(3800-280 x)]:}"The number of shirts Sold ... See the full answer