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Maximizing profit given cost and demand functions

  1. Mar 25, 2012 #1
    1. The problem statement, all variables and given/known data

    If
    C(x) = 13000 + 600x − 0.6x62 + 0.004x3 is the cost function and
    p(x) = 1800 − 6x is the demand function, find the production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)

    2. Relevant equations

    R(x)=xp(x)

    3. The attempt at a solution
    Because of the hint, How I thought this question should be answered was to find the revenue function and take the derivative of that which is the marginal revenue and then set it equal to the derivative of the cost function which is marginal cost
    So,
    R(x)=x(1800-6x)
    R(x)=1800x-6x^2
    R'(x)=1800-12x

    C'(x)=600-1.2x+.012x^2
    1800-12x=600-1.2x+.012x^2
    1200=10.8x+.012x^2
    1200=.012x(900+x)
    100,000=x(900+x)
    100,000=900x+x^2

    is this right? Where do I go from here, can I solve for x at this point? If so how?
     
  2. jcsd
  3. Mar 26, 2012 #2
    what mathematical function are you trying to maximize?
     
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