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Math Help - Urgent Calculus help needed?

  1. #1
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    Urgent Calculus help needed?

    Differentiation

    Profit for a monopolist`s product, the cost function is
    c=0.004q^3(to the power 3) + 20q + 5000

    and the demand function is
    p=450 - 4q

    Find the profit-maximizing output
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  2. #2
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    profit is given by pq-c=(450 - 4q)q-0.004q^3 - 20q - 5000 = 0.004q^3-4q^2+430q-5000

    Differentiate with respect to q and get

    0.012q^2-8q+430.

    Now set this equal to 0 and apply the quadratic formula,
    q=(8-sqrt(8-4*0.012*430))/(2*0.012) or q=(8+sqrt(8-4*0.012*430))/(2*0.012).

    The second isnt possible as there p<0, so your answer is q=(8-sqrt(8-4*0.012*430))/(2*0.012)
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  3. #3
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    Thanks so much Batman!

    Am doing self study and not so good with maths as am preparing for the pre-entry exam for the management finance, could you break it down in detail?
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