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Math Help - Maximum Profit and Minimum Cost(BIG ONE)

  1. #1
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    Question Maximum Profit and Minimum Cost(BIG ONE)

    You are given the function p(q) at which q units of a particular commodity can be sold and the total cost c(q) of producing the q units: In each case

    A)Find:
    Revenue Function R(q), the profit function P(q), the marginal revenue R'(q), and the marginal cost C'(q). Sketch the graphs of p(q), R'(q), and C'(q) on the same coordinates axes and determine the level of production q where P(q) is maximized.

    B)Find:
    Average Cost A(q)=C(q)/q and sketch the graphs pf A(q), and the marginal cost C'(q) on the same axes. Determine Level of Production q at which A(q) is minimized.

    I have the answers because its an odd question and the answers are in the back of the book..but I would like to know how they got the answers....If you can help sure appreciate it...have a bunch of these on my HW for next weak.
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  2. #2
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    Quote Originally Posted by lisa1984wilson View Post
    You are given the function p(q) at which q units of a particular commodity can be sold and the total cost c(q) of producing the q units: In each case

    A)Find:
    Revenue Function R(q), the profit function P(q), the marginal revenue R'(q), and the marginal cost C'(q). Sketch the graphs of p(q), R'(q), and C'(q) on the same coordinates axes and determine the level of production q where P(q) is maximized.

    B)Find:
    Average Cost A(q)=C(q)/q and sketch the graphs pf A(q), and the marginal cost C'(q) on the same axes. Determine Level of Production q at which A(q) is minimized.

    I have the answers because its an odd question and the answers are in the back of the book..but I would like to know how they got the answers....If you can help sure appreciate it...have a bunch of these on my HW for next weak.
    Alright economics time,

    Revenue is Quantity of items sold* Price of items, so Revenue=P*Q which in this case is p(q)*q=(49-q)q= 49q-q^2

    Marginal Revenue=R'(q)=49-2q

    Profit is equal to Revenue-Cost, so it is 49q-q^2-\frac{1}{8q^2}-4q-200=45q-q^2-\frac{1}{8q^2}-200

    Marginal cost=c'(q)= 45-2q+\frac{1}{4q^3}

    Profit is maximized when marginal revenue=marginal cost so set the equations equal and find q
    Last edited by artvandalay11; June 7th 2009 at 06:55 PM. Reason: i now have the equations to give the answers
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  3. #3
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    sorry I forgot to put the function on: its p(q)=49-q; C(q)=1/(8q^2)+4q+200

    Can someone show me how to do this step by step because I missed classes because of the flu so I have not learned how to do these yet.
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