Linear Programming In C#

Question

Hello everybody, i need your help to solve this in c#:

X14 + X24 + X34 + 30 lambda = 130
X14 + X24 + X34 - 10 lambda = 90
X14 + X23 + X33 + 10 lambda = 100
X14 + X23 + X33 - 20 lambda = 70
X13 + X23 + X32 + 15 lambda = 95
X13 + X23 + X32 - 10 lambda = 70
X12 + X22 + X31 + 10 lambda = 80
X12 + X22 + X31 - 10 lambda = 60
X12 + X21 + X32 + 5 lambda = 65
X12 + X21 + X32 - 10 lambda = 60
X11 + X21 + X31 = 60
X14 + X24 + X34 = 150
X12 - X11 = 4
X13 - X12 = 4
X14 - X13 = 4
X22 - X21 = 4
X23 - X22 = 4
X24 - X23 = 4
X32 - X31 = 4
X33 - X32 = 4
X34 - X33 = 4
Xij =  0 (i = 1,2, ... , m ; j = 1,2, ... , n)

How do i solve this problem in c# winforms ?
i am confused, how i can get the answer /value for each data ( lambda ,  x11, x12, 13, etc )

Please help me.
Thank you.
Have a great day. :)