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    Determining optimal production level

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    If total cost function and demand function are as under,

    TC = 10,000 + 100Q + 0.02Q^2
    Qd =20,000 - 100 P

    how do I determine the short-run profit maximizing price and quantity? How do I determine the maximum profit accruable to the firm ?

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    https://brainmass.com/math/graphs-and-functions/determining-optimal-production-level-296421

    Solution Preview

    Solution:

    TC=10000+100Q+0.02Q^2

    Marginal cost can be found by differentiating TC with respect to Q.
    MC=d(TC)/dQ=100+0.04Q

    Now Q=20000-100P
    On rearranging, we ...

    Solution Summary

    Solution depicts the steps to calculate profit maximizing output and price level. It also calculates maximum profit.

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