# Math Help - Finding LP dual for this general LP problem

1. ## Finding LP dual for this general LP problem

I have this LP problem:

max (x1-2x2)

subject to:

x1 + 2x2 - x3 + x4>=0
4x1 + 3x2 + 4x3 - 2x4<=3
-x1 - x2 + 2x3 + x4=1

end

x2,x3>=0 and x1 and x4 are uncontrained

and i am trying to figure out the dual, i arrived to this:

min 3x2+x3

subject to

x1+4x2-x3 = 1
2x1+3x2-x3>=-2
-x1+4x2+2x3>=0
x1-2x2+x3=0

end

The problem is that the optimums are not equal. I am a beginner when it comes to LP and i think i'm missing a simple thing there. Where's the catch?

2. $x_3$ and $x_4$ are unrestricted in sign.

So take

$x_3=x'_3-x''_3$ ; where $x'_3 \;and \;x''_3\geq 0$

and

$x_4=x'_4-x''_4$ ; where $x'_4 \;and \;x''_4\geq 0$

and solve..

3. Yes you can find the dual in that way too, my question is why does the results for the optimum are different considering that the primal is bounded and feasible?