# Thread: Equations for F(x) Help!!!

1. ## Equations for F(x) Help!!!

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.
a.We all know that total revenue (TR) is a function of the price we charged (P) multiplied by the item quantity sold (in our case – Cups), i.e., TR = Price * Cups
c. What price would maximize your TR?

2. Originally Posted by SalsaSoul76
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.
a.We all know that total revenue (TR) is a function of the price we charged (P) multiplied by the item quantity sold (in our case – Cups), i.e., TR = Price * Cups
c. What price would maximize your TR?
You have two points that will lie on your function:

$(C, P) = (2, 120)$ and $(C, P) = (3, 60)$.

To have a linear function of the form

$P = aC + b$, you will need to work out $a$ (the gradient) and $b$ (the P-intercept).

$a = \frac{P_2 - P_1}{C_2 - C_1}$

$= \frac{60 - 120}{3 - 2}$

$= \frac{-60}{1}$

$= -60$.

So you have $P = -60C + b$.

You know that $(2, 120)$ lies on the function, so

$120 = -60(2) + b$

$120 = -120 + b$

$b = 240$.

So the function is $P = -60C + 240$.