1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Is bases the same as basis ? (Simplex Algorithm)

  1. Sep 24, 2011 #1
    1. The problem statement, all variables and given/known data

    [PLAIN]http://img193.imageshack.us/img193/3662/unledmcg.png [Broken]



    3. The attempt at a solution

    I rewrote the whole thing in dictionary

    [tex]x_3 = 15 - 8x_1 - 4x_2[/tex]
    [tex]x_4 = 7 - 2x_1 - 6x_2[/tex]
    [tex]z = 0 + 22x_1 - 12x_2[/tex]

    [tex]x_i \geq 0 [/tex]
    [tex]1\leq i \leq 4[/tex]



    a) So my basis/bases is x = (x_3,x_4)

    b) Do I have to solve the above using the Simplex Algorithm first?

    c) I have to set x_1 or x_2 = 0 and the other one not 0.

    So doing so I get (I chose x_1 and let x_2 = t)

    [tex]x_3 = 15 - 4x_2[/tex]
    [tex]x_4 = 7 - 6x_2[/tex]
    [tex]z = -12x_2[/tex]

    So I get a line of

    x = (0,t|15-t,7-6t)^t

    So my answer is a line with [tex]t \in (-\infty, \frac{7}{6})[/tex]

    I have infinity in my interval...something does not feel right
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Sep 24, 2011 #2

    Fredrik

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Bases is the plural of basis. One basis, two bases. I have to go and do something else now, so I don't have time to help you with the actual problem, but I'm sure someone else will.
     
  4. Sep 24, 2011 #3
    How could there be more than one basis for any LOP?
     
  5. Sep 28, 2011 #4
    I need to make a correction

    When they mean bases, they just mean all combination of the basic variables.

    I happen to have 4 variables and I could only only choose 2 slacks, so that's 6 combination namely

    [tex]\beta = \left \{ 1,2 \right \}, \left \{ 1,3 \right \}, \left \{ 1,4 \right \}, \left \{ 2,3 \right \}, \left \{ 2,4 \right \}, \left \{ 3,4 \right \}[/tex]
     
  6. Oct 2, 2011 #5
    I just have one question, it's given that at least one basic solution HAS to be an optimal right? There can't be two optimal?
     
  7. Oct 2, 2011 #6

    Pyrrhus

    User Avatar
    Homework Helper

    There may be multiple optimal solutions, but yes at least one (if the Weierstrass theorem is satisfied).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Is bases the same as basis ? (Simplex Algorithm)
  1. Simplex method (Replies: 0)

  2. Simplex Problem (Replies: 1)

Loading...