A coffee shop currently sells 410 lattes a day at $3.00 each. They recently tried raising the by price by $0.25 a latte, and found that they sold 40 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 $? _