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    Profit Function and Maximum Profit

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    A manufacturer finds that the total profit from producing and selling Q units of a product is given by the profit function:

    Total Profit = f(Q) = - 460 + 100Q - Q^2

    1. Compute the value of the function at Q=10

    Total Profit = f(10)= - 460 + 100(10) - 10^2
    Total Profit = f(10)= - 460 + 1000 - 100
    Total Profit = f(10)=540 - 100
    Total Profit = f(10)=440

    2. Compute the value of the first derivative of the function at Q=10

    3. Explain the significance of each computation.

    4. At what level of Q is Profit equal to 1,815?

    5. Use Calculus: At what level of Q will Total Profit be a maximum?

    6. Double-check your answer to part 5 with an Excel graph.

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    A manufacturer finds that the total profit from producing and selling Q units of a product is given by the profit function:

    Total Profit = f(Q) = - 460 + 100Q - Q^2

    1. Compute the value of the function at Q=10

    Total Profit = f(10) = - 460 + 100(10) - 10^2
    Total Profit = f(10) = - 460 + 1000 - 100
    Total Profit = f(10) = 540 - 100
    Total Profit = f(10) = 440

    2. Compute the value of the first derivative of the ...

    Solution Summary

    The expert examines profit functions and maximum profits.

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