math

a distributor of apple juice has 5000 bottle in the store that it wishes to distribute in a month. from experience it is known that demand D (in number of bottles) is given by D = -2000p² + 2000p + 1700. the price per bottle that will result zero inventory is

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asked by nithin
  1. just solve for p in

    -2000p² + 2000p + 1700 = 5000

    The problem is that D has a maximum of 2200 when p = 0.5

    I suspect a typo somewhere. Is D the monthly demand, or the weekly demand?

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    posted by Steve
  2. let D=5000

    D=-2000p^2+2000p+17000
    5000=-2000p^2+2000p+17000
    divided by 1000
    5=-2p^2+2p+17
    5-17=-2p^2+2p
    -12=-2p^2+2p
    2p^2-2p-12=0
    divided by 2
    p^2-p-6=0
    p^2-3p+2p-6=0
    p(p-3)+2(p-3)=0
    (p-3) (p+2)=0
    p-3=0 p+2=0
    p=3 p=-2

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