A company’s marginal revenue function is given as MR(x) = 5000 – 100x. Find the total revenue function and the total revenue maxim

A company’s marginal revenue function is given as MR(x) = 5000 – 100x. Find the total revenue function and the total revenue maximizing output.

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  1. Given : A company’s marginal revenue function is given as MR(x) = 5000 – 100x

    To Find : the total revenue function and the total revenue maximizing output.

    Solution:

    The marginal revenue is the derivative of the revenue function

    MR(x) = 5000 – 100x

    integrating

    R(x) = 5000x – 100x²/2 + C

    => R(x) = 5000x – 50x² + C

    C is constant

    at x = 0 Revenue is 0

    Hence R(0) = 0 – 0 + C = 0

    => C = 0

    Hence R(x) = 5000x – 50x²

    Hence total revenue maximizing output is when 5000x -50x² is max

    R'(x) = 5000 – 100x

    R'(x) = 0

    => 5000 – 100x = 0

    => x = 50

    R”(x) = – 100 < 0

    Hence maximum when x = 50

    total revenue maximizing output. is 50

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