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18 September, 00:47

4. The revenue of a company for a given month is represented as? (x) = 1,500x - x^2 and its costs as? (x) = 1,500 + 1,000x.

What is the selling price, x, of its product that would yield the maximum profit? Show or explain your answer.

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  1. 18 September, 02:10
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    The profit will be maximum on x = 250.

    Step-by-step explanation:

    From the given information:

    Revenue = 1500x - x²

    Cost = 1500 + 1000x

    As we know that

    Profit = Revenue - Cost; Let say it equation 1

    Then after putting the values of revenue and cost in equation 1 we have:

    Profit = (1500x - x²) - (1500 + 1000x)

    Profit = 1500x - x² - 1500 - 1000x

    Profit = - x² + 500x - 1500

    We know that at the max or min the slope of the graph formed by the profit function will be zero, therefore we find the slope of profit function by taking the first derrivative w. r. t. x as under:

    d (Profit) / dx = d/dx (-x² + 500x - 1500)

    d (Profit) / dx = - 2x + 500

    By putting the above slope equal to zero we get:

    d (Profit) / dx = - 2x + 500 = 0

    -2x + 500 = 0

    -2x = - 500

    x = 250

    Therefore it is concluded that the profit will be maximum when x will be equal to 250.
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