i want to solve this problem , i solved it by lingo and output is :
$z^*=540; X11 = 1.666667 , X21= 32.22222 , X12 = 33.33333 , X22 =0.000000$
when i solved this problem by Dantzig–Wolfe decomposition decomposition i get $z^*=540; X11=X22=0, X12=X21=\frac{100}{3}$
but in two case ,when substitute solution in $Z$ we dont have $Z=540$ !!
substitute lingo solution in Z we have Z= 535.55
and when my solution substitute in Z , we have Z=533.33
why?
how can solve this problem by Dantzig–Wolfe decomposition,i think my solution is wrong?
$\max z= 8*x11 + 6*x21 + 10*x12+8*x22$
$s.t.$
$ 2*x11+3*x21 <=100$
$3*x12+4*x22 <=100$
$x11+x12 <=35$
$x21+x22<=35$
$X11,X12,X21,X22 >=0$