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

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    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?
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  2. #2
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    Quote Originally Posted by SalsaSoul76 View Post
    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 $\displaystyle P = -60C + 240$.
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