A coffee shop currently sells 370 lattes a day at $2.75 each. They recently tried raising the 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 $