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Math Help - [SOLVED] Revenue Equation help

  1. #1
    Space Comet
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    [SOLVED] Revenue Equation help

    Please help!!! Here is the problem:

    The profit p (in thousands of dollars) on x thousand units of a specialty item is p = 0.8x - 15.5. The cost c of manufacturing x items is given by c = 0.6x + 15.5 .


    Find an equation that gives the revenue r from selling x items.




    How many items must be sold for the company to break even (i.e., for revenue to equal cost)?

    Round to the nearest integer.
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  2. #2
    Senior Member topher0805's Avatar
    Joined
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    Profit is revenue minus the cost, so:

    p = r - c

    Therefore, to find the revenue we have:

    r = p + c

    So we add the two equations:

    <br />
(0.8x - 15.5) + (0.6x + 15.5)<br />

    To get:

    1.4x

    Therefore, r = 1.4x

    To find when you will break even, simply set the two equations equal to each other:

    1.4x = 0.6x + 15.5

    To get:

    0.8x = 15.5

    Therefore, x = 19.375


    Note that another way of finding when you will break even is to set the profit equal to 0:

    0.8x - 15.5 = 0

    Which gives you the same result:

    <br />
x = 19.375
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