Math Help - 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:

$(C, P) = (2, 120)$ 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 $P = -60C + 240$.