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Thread: Linear Programming - Vertex Enumeration

  1. #1
    Jan 2011

    Exclamation Linear Programming - Vertex Enumeration

    Linear Programming - Vertex Enumeration-lp.pdf
    Hi, I have the following problem (I have scanned and attached a file of what I have got so far...but I really don't know what I am doing)... It says:

    Write down the following LP problem in standard form by introducing slack variables $\displaystyle x_4$ and $\displaystyle x_5$. And also, use vertex enumeration to identify all vertices of the feasible region and, hence, determine an optimal solution to the problem.

    maximise $\displaystyle f = -x_1 + 4x_2 + 5x_3$
    subject to
    $\displaystyle -x_1 + x_2 + 3x_3 <= 3$
    $\displaystyle 2x_2 + x_3 <= 8$
    $\displaystyle x_1, x_2, x_3 >= 0$

    So this is easy, I got:

    maximise $\displaystyle f= -x_1 + 4x_2 + 5x_3$
    subject to
    $\displaystyle -x_1 + x_2 + 3x_3 + x_4 = 3$
    $\displaystyle 2x_2 + x_3 + x_5 = 8$
    $\displaystyle x_1, x_2, x_3, x_4, x_5 >= 0$

    So what I don't know is when a singular system is inconsistent (I've crossed through 2 rows, but I am not sure...), how you pick the values for the coordinates (there could be much more than 10 combinations and I don't know what I should look for)... and also, do I need to draw the LP problem to see which ones are feasible, or is there any other way I can work it out mathematically?

    I would really appreciate it if you could give me a little explanation so that I can get this done before tomorrow
    Last edited by mbmstudent; Feb 1st 2011 at 04:07 PM. Reason: forgot attaching file
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