Results 1 to 3 of 3

Math Help - Linear Progamming

  1. #1
    Newbie
    Joined
    Feb 2014
    From
    singapore
    Posts
    2

    Linear Progamming

    I need your help to solve the following
    Given $Bx \leq b$ (1)

    Consider the linear programming problem $\max \{1.y:Bx+y-\beta b \leq 0, 0 \leq y \leq 1, \beta \geq 1\}$ (2)


    a. Suppose that (2) is feasible and $(x^*,y^*,\beta^*)$ is an optimal solution. Prove that $y^*_i$ if and only if $B_ix \leq b_i$ is an implicit equality of (1).

    b. Prove that the optimal solution of the linear programming problem (2) determines which inequalities from $Bx \leq b$ are always satisfied with equality.

    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,414
    Thanks
    1853

    Re: Linear Progamming

    What do you mean by "prove y_i^*"? Prove that it has what property?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2014
    From
    singapore
    Posts
    2

    Re: Linear Progamming

    $y^*=(y^*_k)$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear Algebra Linear maps dealing with linear independence.
    Posted in the Advanced Applied Math Forum
    Replies: 4
    Last Post: March 22nd 2013, 03:02 PM
  2. Replies: 3
    Last Post: March 8th 2013, 06:04 AM
  3. Replies: 7
    Last Post: October 10th 2011, 04:06 PM
  4. Linear Progamming on a calculator
    Posted in the Algebra Forum
    Replies: 0
    Last Post: September 20th 2009, 11:22 AM
  5. Integer Progamming Question
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: March 5th 2009, 02:03 PM

Search Tags


/mathhelpforum @mathhelpforum