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 $9 per guest and averaged 320 guests per night. The next week you charged $11 per guest and averaged 280 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 $3 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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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.