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Cost of Manufacturing X Items (average cost minimization)

  1. Nov 16, 2011 #1
    1. The problem statement, all variables and given/known data
    If the cost of manufacturing x items is:
    C(x) = (x^3)+21(x^2)+110x+20



    2. Relevant equations

    All right, so the first few questions asked for total cost of producing 100 items, and marginal cost. I understood those well. Then it asked for the average cost function, which I found to be C(x)/x. I have a problem where it asks "The production level when the average cost is minimized."


    3. The attempt at a solution
    Well, I would take the derivative of the average cost function (C(x)/x)
    which would give me (2(x^3)+21(x^2)-20)/(x^2)

    So then we set that equal to zero, I'm stuck at setting the top equal to zero. How can I factor it? I graphed the average cost function and found x to be approximately -10.40768.
    Is there any way to factor it? Or do I have to use a calculator?


    Thank you in advance for your replies.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 16, 2011 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You get a cubic equation having two negative roots and one positive root. There are formulas available for solving cubic equations, but they are rarely used. A numerical method is preferable in this case. Only positive roots make sense in this problem: we cannot have a negative production level!

    RGV
     
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