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Derivatives in Economics problem

  1. Feb 25, 2010 #1
    1. The problem statement, all variables and given/known data
    The cost in dollars for producing x units is given by C(x) = 1.22x+ 2500 . The demand curve is given by p(x) = (60,000-x)/(10,000)

    A. Find the revenue function R(x) in simplest form.

    B. Find the marginal revenue function and the marginal revenue for selling 15000 units.

    C. Find the profit function P(x) in simplest form.

    D. Find the marginal profit function in simplest form.

    E. Find the marginal profit for selling 23,700, 23,900 and 24,000 units.

    F. Find the average cost function in simplest form

    G. Find the marginal cost function. What is the marginal cost of 2000 units?


    2. Relevant equations



    3. The attempt at a solution
    I'm not sure how to get equations for the functions it asks for. I honestly have no idea how to even begin this question. If someone could explain how I can take the given info and turn it into revenue, profit, etc. then I can hopefully do the rest. Thank you for your help!
     
  2. jcsd
  3. Feb 26, 2010 #2
    Let's start with A. What is the definition of revenue? Recall what x and p(x) represent.
     
  4. Feb 26, 2010 #3
    What do you think about these answers guys:

    The cost in dollars for producing x units is given by C(x) = 1.22x+ 2500 . The demand curve is given by p(x) = (60,000-x)/(10,000)

    A. Find the revenue function R(x) in simplest form.
    Answer: R(x)=p(x)x
    =6(x)2

    B. Find the marginal revenue function and the marginal revenue for selling 15000 units.
    R'(x)=6x2
    =12x

    C. Find the profit function P(x) in simplest form.
    P(x)=R(x)-C(x)
    =6x2-1.22x+2500

    D. Find the marginal profit function in simplest form.
    P'(x)=R'(x)-C'(x)
    =12x-1.22

    E. Find the marginal profit for selling 23,700, 23,900 and 24,000 units.
    E1) 12(23,700)-1.22 = 284,398.78
    E2) 12(23,900)-1.22 = 286,798.78
    E3) 12(24,000)-1.22 = 287,998.78

    F. Find the average cost function in simplest form
    (1.22x+2500)/x
    = 1.22+(2500/x)

    G. Find the marginal cost function. What is the marginal cost of 2000 units?
    C'(x)=1.22x+2500
    =1.22
    Therefore the marginal cost for producing 2000 units is also 1.22.
     
  5. Feb 26, 2010 #4
    Check your work. Does [(60000 - x)/10000]x = [6 - x/10000]x equal 6x^2?
     
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