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Thread: Revenue Function

  1. #1
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    Revenue Function

    I dont understand this question. Can you please tell me how to do the question, and help me with doing it?

    The demand function for snack cakes at a large bakery is given by the function $\displaystyle p(x) = \frac{15}{2x^2+11x+5}$. The $\displaystyle x$-units are given in thousands of cakes, and the price per snack cake, $\displaystyle p(x)$, is in dollars.

    a) Find the revenue function for the cakes

    b) Estimate the marginal revenue for $\displaystyle x=0.750$. What is the marginal revenue for $\displaystyle x=2.00$?
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by haddad287 View Post
    I dont understand this question. Can you please tell me how to do the question, and help me with doing it?

    The demand function for snack cakes at a large bakery is given by the function $\displaystyle p(x) = \frac{15}{2x^2+11x+5}$. The $\displaystyle x$-units are given in thousands of cakes, and the price per snack cake, $\displaystyle p(x)$, is in dollars.

    a) Find the revenue function for the cakes

    b) Estimate the marginal revenue for $\displaystyle x=0.750$. What is the marginal revenue for $\displaystyle x=2.00$?
    The revenue function is R(x) = quantity * price = x * p(x).

    Marginal Revenue refers to R'(x), the first derivative of Revenue.

    Good luck!
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  3. #3
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    What do you mean by "R(x) = quantity * price = x * p(x)." ???

    Please explain that more
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  4. #4
    Senior Member apcalculus's Avatar
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    Sure:

    revenue = price times quantity

    Example:
    You sell 20 cds at ten dollars each:

    x = quantity = 20 cds
    p(x) = $10
    R(x) = revenue = x * p(x) = 20 * 10 = 200
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  5. #5
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    Thank you, but for some reason, the answer is soppsoe to be $\displaystyle
    R(x) = \frac{15}{2x^2+11x+5}
    $

    That is what it says in the Answers for that question
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  6. #6
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by haddad287 View Post
    Thank you, but for some reason, the answer is soppsoe to be $\displaystyle
    R(x) = \frac{15}{2x^2+11x+5}
    $

    That is what it says in the Answers for that question
    That's the price function; the revenue function is product of the price function with quantity x, so if you throw in an x, you get revenue:

    $\displaystyle
    R(x) = x \times p(x) = x \times \frac{15}{2x^2+11x+5} = \frac{15x}{2x^2+11x+5}
    $
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