The notation is as follows. Let the network (N, A) be an oriented graph consisting of a number of nodes and edges with a given direction, indexed by $n∈ N = {1, ..., N}$ and $(n,m)∈ A \subset {(n,m) :n,m∈ N,n≠m}$}. A node corresponds to a location in the network and an edge to a transmission connection (i.e. a cable) between two nodes. Each node has a given net supply such that $d_n> 0$ (measured in MWh) if the node offers more than it demands, $d_n <0$ if inverse and $d_n = 0$ if the node is merely for transit. Each edge (n, m) is connected to a transmission cost $c_{nm}$ (DKK(danish money) / MWh). The net supply and costs are parameters, whereas the transmission on the edges is represented by decision variables. The transmission on edge (n, m) is denoted as $l_{nm}$ (MWh).
The graph indicates data for the network problem. The number on the edge (n, m) indicates costs, $c_{nm}$, and the number at the node indicates supply or demand, $d_n$ ($d_n$> 0 indicates supply and $d_n$ <0 indicates demand). A stretchy tree is marked with bold edges.
Assume there are capacity constraints on transmission connections. Let $l^{max}_{nm}$ denote the capacity on edge (n, m) (in MW).
I have to write the general network problem with capacity constraints as a linear programming problem (LP-problem), but how can I do that?