Duality of a linear programming problem in matrix form? trying to find the duality of the LP problem in matrix/vector form:
min c1Tx1 + c2Tx2
s.t.    A1x1 + A2x2 = b
x1>= 0
I get that the duality of like  
min cTx
s.t. Ax = b
x>=0   
would be  
max bTu
s.t. ATu <= c  
but I'm not really sure how the addition of 2 different matrices would affect the constraints or how to visualize this problem? I think the objective would still be max bTu but I am not sure?
Thanks.

I assume that $x_1$ and $x_2$ are single variables. Then the dual program is
$\texttt{max} \ \ b^Tu$
$A_1^T u\leq c_1$
$A_2^T u=c_2$
The number of variables ($u_i$) depends on the dimension of vector $\mathbf b$.
