Expert: Bobby Soltani - 7/11/2009

Question
Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 120 cups.  But when you raise your price to $3 you only sell 60 cups.  

a.    Write an equation for the number of cups you sell as a function of the price you charge.  

b.    Denote "C" for number of cups, and "P" for the price you charge.

c.    Assume the function is linear.  

Answer
Hi Gregory,

a.    Write an equation for the number of cups you sell as a function of the price you charge.  

We are given two data points (P,C).  The first data point is (2, 120), and the second one is (3,60).

Solution: Let the linear function be C(P) = Pa + b, where a and b are constants to be determined.
When P = $2, C = 120, 120 = 2a + b …………….equation (i)
When P = $3, C = 60, 60 = 3a + b …………..equation (ii)
Subtracting (i) from (ii), we get a = -60
Plugging in a = -60 in (i), we get b = 240
Thus, the function is C(P) = -60P + 240
You can plug in the two data points to check the answer.

Let me know if you have any questions.

Bobby