Hope it's okay to ask this here?

Discussion in 'Personal Homework Help' started by Gijoefan1976, Apr 30, 2017.

  1. Gijoefan1976

    Gijoefan1976 New Member

    A candy vendor analyzes his sales records and finds that if he sells x candy bars in one day, his profit(in dollars) is given byP(x) = − 0.001x2 + 3x − 1800
    (a.) Explain the significance of the number 1800 to the vendor.
    (b.) What is the maximum profit he can make in one day, and how many candy bars must he sell to
    achieve it?

    I got 1800 as the amount he starts with, and can't go over. maximum profit as 4950

    and if I got that right I am getting stuck on how to find how many candy bars.


  2. math_celebrity

    math_celebrity Administrator Staff Member

    a) 1800 is the cost to run the business for a day. To clarify, when you plug in x = 0 for 0 candy bars sold, you are left with -1,800, which is the cost of doing business for one day.

    b) Maximum profit is found by taking the derivative of the profit equation and setting it equal to 0.
    P'(x) = -0.002x + 3

    With P'(x) = 0, we get:
    -0.002x + 3 = 0

    Using our equation solver, we get:
    x = 1,500

    To get maximum profit, we plug in x = 1,500 to our original profit equation
    P(1,500) = − 0.001(1,500)^2 + 3(1,500) − 1800
    P(1,500) = -2,250 + 4,500 - 1,800
    P(1,500) = $450

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