# Finding LP dual for this general LP problem

• November 12th 2009, 01:28 PM
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?
• November 13th 2009, 05:57 AM
kjchauhan
$x_3$ 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..
• November 14th 2009, 05:17 AM