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Calculus

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it is assumed that the toothpaste market is perfectly competitive and the current price of a case of toothpaste is 42.00. CPI (the company) has estimated its marginal cost function to be as follows: MC (Marginal Costs) =.006Q (Quantity).
The board would like to know how many cases of toothpaste should be produced in order to maximize profits

  • Calculus -

    In calculus terms,
    Profit=P(q)=42q-0.006q*q
    dP(q)/dq = 42-0.012q = 0
    q=42/0.012=3500 cases.

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