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?