It costs Charlie $19 to build a certain birdhouse. If he charges x dollars per birdhouse, he can sell 58−3x birdhouses per week. ?

Find a function for his weekly profit.

1 Answer

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  • 1 month ago

    Profit is the difference bewteen the revenue and costs:

    P(x) = R(x) - C(x)

    If he can sell (58 - 3x) birdhouses a week at "x" dollars each, the revenue is the product:

    R(x) = x(58 - 3x)

    R(x) = -3x² + 58x

    The cost is $19 times the number of birdhouses (58 - 3x) so:

    C(x) = 19(58 - 3x)

    C(x) = -57x + 1102

    Substitute and simplify:

    P(x) = R(x) - C(x)

    P(x) = (-3x² + 58x) - (-57x + 1102)

    P(x) = -3x² + 58x + 57x - 1102

    P(x) = -3x² + 115x - 1102

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