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Math Help - Refrigerator consumption

  1. #1
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    word problem

    The monthly demand model for a refrigerator is given by N = -8p + 20000. The monthly supply model for the same refrigerator is N = 10p + 4250. For these models, p is the price of the refrigerator and N is the number of refrigerators sold or supplied each month by the store. Find the price at which supply and demand are equal (break-even point). At this price, how many refrigerators can be supplied and sold each month?

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  2. #2
    MHF Contributor
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    Monthly demand: Nd = -8p + 20000.

    Monthly supply: Ns = 10p + 4250

    When the two are equal,
    Nd = Ns
    -8p +20,000 = 10p +4,250
    20,000 -4,250 = 10p +8p
    15,750 = 18p
    p = 15,750 / 18
    p = 875 -------***

    That means at break-even point, the price per refrigerator is 875. (in dollars or whatever. Not mentioned in the problem.)

    ----------------------------------
    Substitute that in, say, Nd,
    Nd = -8(875) +20,000 = 13,000

    In Ns,
    Ns = 10(875) +4,250 = 13,000 ----same, OK.

    Therefore, at brake-even point, 13,000 refrigerators have to be supplied and sold at 875 each.
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