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Math Help - functions

  1. #1
    Junior Member
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    Post functions

    Hello,
    I've been studying for my test and got stuck on this question, can anybody explain it to me?

    The demand function for a new product is P(x) = -5x + 22 where x is the number of items sold in thousands and p is the rice in dollars. The cost function is
    C(x) = 3x + 15.
    a) state the corresponding revenue function (I'm pretty sure it's -5x^2 + 22x)
    b) Find the corresponding profit function(I'm having problem with that)
    c) Complete the square to find the value that will maximize the profits.
    d) Find the break even quantities.

    Thank you,
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  2. #2
    MHF Contributor
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    The demand function for a new product is P(x) = -5x + 22 where x is the number of items sold in thousands and p is the price in dollars.
    Umm. Shouldn't that be called the price function?


    a) state the corresponding revenue function (I'm pretty sure it's -5x^2 + 22x)
    Yes, it is.
    Because revenue is (demand)*(price).

    b) Find the corresponding profit function(I'm having problem with that)
    Profit = Revenue -Cost
    So,
    Profit(x) = (-5x^2 +22x) -(3x +15)
    Profit(x) = -5x^2 +19x -15 ---------------------answer.

    c) Complete the square to find the value that will maximize the profits.
    -5x^2 +19x -15
    = -5[x^2 +(19/5)x +3]
    = -5[x^2 +(19/5)x +(19/10)^2 -(19/10)^2 +3]
    = -5[(x +(19/10))^2 -(19/10)^2 +3]

    So, the x at maximum profit is -19/10
    What?
    Negative demand? No product?

    There is something wrong with your Question as posted.

    Edit:
    Oopps, my mistake!
    It should have been:
    -5x^2 +19x -15
    = -5[x^2 -(19/5)x +3]
    = -5[x^2 -(19/5)x +(19/10)^2 -(19/10)^2 +3]
    = -5[(x -(19/10))^2 -(19/10)^2 +3]
    So the x at maximum profit is 19/10 thousand = 1900 products

    Therefore, to maximize profit, 1900 of the products must me made. ---------------answer.

    d) Find the break even quantities.
    At break-even, the profit is zero because the revenue equals the cost only.

    So,
    -5x^2 +22x = 3x +15
    -5x^2 +22x -3x -15 = 0
    -5x^2 +19x -15 = 0
    Divide both sides by -5,
    x^2 -3.8x +3 = 0
    Use the Quadratic formula,
    x = {3.8 +,-sqrt[(3.8)^2 -4(1)(3)]} / 2(1)
    x = {3.8 +,-1.562} /2
    x = 1.119 or 2.681 thousands product.

    Therefore, it is break-even if 1,119 products or 2,681 products are made. -------------answer.
    Last edited by ticbol; October 6th 2007 at 04:08 PM.
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  3. #3
    Junior Member
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    Thank you very much.
    That was exactly what I was looking for.
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