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Math Help - Optimization in economic question

  1. #1
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    Optimization in economic question

    A firm that produces a single product faces a demand function : q = 10,000P - 100P where q is the quantity demanded, and p is the firmís price. Its total cost function is : TC(q)= 200+20q+q2/300.
    the question is : What is the profit-maximising level of production for this firm? answer= q=3000
    What is the firmís maximum profit? R= 119800
    Calculate (discrete) marginal revenue and (discrete) marginal cost at an output of 2000 ?. MR=60 , Mc= 33.3

    The correct answers are in brackets after the question , but I am more interested in explaining how the answer was obtained. with thanks
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  2. #2
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    Re: Optimization in economic question

    Hey SAM123.

    What is this total cost function? How do you identify profit in this model?
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  3. #3
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    Re: Optimization in economic question

    Total Cost function : TC(q)= 200+20q+q2/300.
    Write a formula for profit (π) in terms of q.
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