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Math Help - Cornerpoints of solution region of linear system.

  1. #1
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    Cornerpoints of solution region of linear system.

    I am having trouble finding the cornerpoints of the solution region of a linear system. There seems to be discrepancy between the graph of the solution region and the cornerpoints I can find algebraically.

    Here is the linear system:
    x, y ≥0
    1x + 11y ≤ 1
    7x + 2y ≤1

    This is a picture of the linear system plotted on a graph and of the system's small bounded solution region:
    Cornerpoints of solution region of linear system.-solution-region.png

    The cornerpoints that I have obtained algebraically are:

    (i) for the intersection of y = 0 and x = 0, (0, 0)
    (ii) for the intersection of y = 0 and 7x + 2y = 1, (1/7, -1/2)
    (iii) for the intersection of x = 0 and 1x + 11y = 1, (1,0)
    (iv) for the intersection of 1x + 11y = 1 and 7x + 2y = 1, (8.3, -0.7)

    Those cornerpoints don't seem to be right according to the bounded region in the graph.
    Here is an example of how I algebraically came to a cornerpoint:

    Intersection of 1x + 11y = 1 and 7x + 2y = 1

    (1-7x)/2 = (1-1x)/11
    11(1-7x) = 2(1-1x)
    11 - 77x = 2 - 2x
    11 - 77x - 2 + 2x = 0
    9 - 75x = 0
    -75x = -9
    x = 8.333333333

    1(8.333333333) + 11y = 1
    8.333333333 + 11y = 1
    11y = -7.333333333
    y = -0.666666666 or -0.7
    Attached Thumbnails Attached Thumbnails Cornerpoints of solution region of linear system.-solution-region.png  
    Last edited by Yoodle15; February 3rd 2013 at 12:33 PM.
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: Cornerpoints of solution region of linear system.

    Hi Yoodle15!

    Quote Originally Posted by Yoodle15 View Post
    -75x = -9
    x = 8.333333333
    Could you calculate that again?
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  3. #3
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    Re: Cornerpoints of solution region of linear system.

    \frac{9}{75}= \frac{3(3)}{3(25)}= \frac{3}{25}= \frac{3(4)}{25(4)}= \frac{12}{100}
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  4. #4
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    Re: Cornerpoints of solution region of linear system.

    Such a silly mistake on my part! Thank you for pointing it out to me! *feels silly*
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  5. #5
    Super Member ILikeSerena's Avatar
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    Re: Cornerpoints of solution region of linear system.

    No problem. Cheers!
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