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I'm having some troubles to continue solving my system, I'm used to solve such systems but with "one" binding constraint, if someone could give me some helpful hints so I can solve it I will be grateful.

Here is the problem:

Solve the following LP using the Dantzig-Wolfe method:

LP

This is what I have done so far:

We may notice that there are 6 constraints, and the 2 first constraints will be binding constraints.

  • The matrix form of the problem (P) is:

Matrix form of (P)

Hence:

Matrix A

And:

Matrix B

And:

Matrix C

It is a two-block structure.

i = 1 Constraints block (3) and (4)

i = 2 Constraints block (5) and (6)

Constraints 1 and 2 are binding constraints.

D1

D2

b1

b2

c1

c2

My question is: What can I do so I could solve this problem?

Improve this question
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  • $\begingroup$ Welcome to OR.SE, I think the last constraint should be $2x_3 + x_4 \leq 10$. $\endgroup$
    – Oguz Toragay
    Feb 24 at 16:05
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    $\begingroup$ I suggest that you refer to the first two constraints as "connecting" constraints rather than "binding" constraints, to avoid confusion. Constraints are "binding" at a particular solution when the slack or surplus is zero at that solution. $\endgroup$
    – prubin
    Feb 24 at 20:25
  • $\begingroup$ Or linking constraints or complicating constraints. $\endgroup$
    – RobPratt
    Apr 7 at 14:18
  • $\begingroup$ Please use MathJax instead of images. Are the variables really $\le 10$ or did you instead mean $\ge 0$? $\endgroup$
    – RobPratt
    Apr 7 at 14:21

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