# Two binding constraints - Linear Programming

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:

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:

Hence:

And:

And:

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.

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

• Welcome to OR.SE, I think the last constraint should be $2x_3 + x_4 \leq 10$. Feb 24 at 16:05
• 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. Feb 24 at 20:25
• Or linking constraints or complicating constraints. Apr 7 at 14:18
• Please use MathJax instead of images. Are the variables really $\le 10$ or did you instead mean $\ge 0$? Apr 7 at 14:21