# 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.
Continuing our lemonade stand question:
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
b.Please write the equation for your TR by inputting your answer from the function you have calculated in question #2.
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.
Continuing our lemonade stand question:
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
b.Please write the equation for your TR by inputting your answer from the function you have calculated in question #2.
c. What price would maximize your TR?
You have two points that will lie on your function:

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

To have a linear function of the form

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

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

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

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

$\displaystyle = -60$.

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

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

$\displaystyle 120 = -60(2) + b$

$\displaystyle 120 = -120 + b$

$\displaystyle b = 240$.

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