1)The market research department of the Better Baby Buggy Co. predicts that the demand equation for its buggies is given by

q = 3.5p + 910

where q is the number of buggies the company can sell in a month if the price is $p per buggy. At what price (in dollars) should it sell the buggies to get the largest revenue?

p = $ ______

What is the largest monthly revenue (in dollars)?

$ =________

2)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 $5 per guest and averaged 375 guests per night. The next week you charged $10 per guest and averaged 300 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.

q(p) =

(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 $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(p) =

(d)Now find the profit in terms of the cover charge p.

P(p) =

e) Determine the cover charge you should charge for a maximum profit (in dollars).

p = $ _____ per guest