Question

A coffee shop currently sells 300 lattes a day at $2.50 each. They recently tried raising the price by $0.25 per latte and found that they sold 50 fewer 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 price per cup by 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 $=

          A coffee shop currently sells 300 lattes a day at $2.50 each. They recently tried raising the price by $0.25 per latte and found that they sold 50 fewer 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 price per cup by 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 $=

Added by Andrew S.

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