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Math Help - Differentiation - Calculus help!

  1. #1
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    Red face Differentiation - Calculus help!

    PROFIT for a monopolist`s product, the cost function is
    c=0.004q^3 + 20q + 5000

    and the demand function is
    p=450 - 4q

    Find the profit-maximizing output.

    Please assist step by step?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Andrew1380 View Post
    PROFIT for a monopolist`s product, the cost function is
    c=0.004q^3 + 20q + 5000

    and the demand function is
    p=450 - 4q

    Find the profit-maximizing output.

    Please assist step by step?
    Revenue is:

     pq =450q -4q^2

    profit is revenue minus costs:

    pr(q)=450q -4q^2 - (0.004q^3 + 20q + 5000)=-0.004q^3-4q^2+430q-50000

    Now find the extrema of this by differentiating and setting the derivative to zero and solving for the critical values of q, the critical value that maximises the profit will be the profit maximising output.

    q=50 and profit=6000
    CB
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