and are unrestricted in sign.
So take
; where
and
; where
and solve..
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?