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Math Help - Price modelling - Simultaneous Linear Equations.

  1. #1
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    Price modelling - Simultaneous Linear Equations.

    I decided to put my new algebra skills into practice recently. But it didn't work!

    I obtained a price list the other day for some products we are looking to buy. Their price decreases the more you buy.

    between 50-99 qty their price is 8.76
    between 100-199 qty their price is 6.57

    There will become a point where it's the same price to buy x amount in the lower price bracket than it would to buy the same money's worth in the higher price bracket. I.e, you'd get more for the same price.

    I tried using linear equations for both prices and solving them simultaneously to find a point of intersection where both equations were equal. But the lines only intersect at 0.

    I know it is possible to do this. I'm just stumbling somewhere. Bit of help would be good. I am thinking I may need to add a value to the constant of the linear equations, but am unsure where to start.
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  2. #2
    Pim
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    There are multiple points where you get more for the same price.
    The prices lie between 99*€8.76=€867.24 and 100*€6.57 = €657
    So, you can get either 99 or x*6.57=867.24 => x = 132 products for €867.24
    but you can also get 100 or x*8.76=657 => x = 75 products for €657
    So, from 77 products and onwards, you should be buying more, as to end up in the higher bracket.
    I used € because can't find how to get pounds on here.
    Also, I realized I did some redundant math, but I decided to leave it there if you might need it/are interested in it.
    Last edited by Pim; August 25th 2010 at 09:36 PM.
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  3. #3
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    Thanks.

    I appreciate your input, however, I think you may have missed my point (probably my poor explanation).

    I know from experimenting with this that it I can buy 100 at 6.57 or 75 8.76.

    I was hoping there was a way to model this, linearly, and solve linearly. More out of curiosity, and dare I say it, fun?

    I know both the prices can be modelled linearly, I just need an equation to do it. In 'my' theory, their lines should intersect at 75?

    Am I trying to do the impossible here?
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  4. #4
    Pim
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    I don't think you can get intersecting lines.
    You could think of this as solving the equation 100*6.57 = x*8.76
    Another way to think about this is as follows
    f(x)=8.76*x

    D_f = 50 \leq x \leq 99

    g(x)=6.57*x

    D_g = 100 \leq x \leq 199

    f(x_1) = g(x_2)

    8.76*x_1=6.57*x_2

    x_1 = 0.75*x_2

    Here you can plug in x_2 = 100
    Therefore you can conclude that
    x_1 = 0.75*x_2 can be (validly) computed for

    75 \leq x_1 \leq 99

    100 \leq x_2 \leq 132

    I must add that I have no idea if this last bit is real mathematics. It's how I imagined you could solve it using equations.
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