A coffee shop currently sells 320 lattes a day at $3.25 each. They recently tried raising the by price by $0.25 a latte, and found that they sold 50 less lattes a day.

a) Assume that the number of lattes they sell in a day, N, is linearly related to the sale price, p (in dollars). Find an equation for N as a function of p.

N(p) =  

b) Revenue (the amount of money the store brings in before costs) can be found by multiplying the cost per cup times the number of cups sold. Again using p as the sales price, use your equation from above to write an equation for the revenue, R as a function of p.

R(p) =  

c) The store wants to maximize their revenue (make as much money as possible). Find the value of p that will maximize the revenue (round to the nearest cent).

p =  
which will give a maximum revenue of $