int: nNoeuds;
int: nAretes;

array[1..nAretes, 1..2] of 1..nNoeuds: A; %Each edge has the form (i,j) where i is the source vertex and j is the destination vertex
array[1..nAretes] of int: u; % capacity of each edge
array[1..nAretes] of int: c; % cost of each edge

int: source;
int: dest;


array[1..nAretes] of var int: x; % Variable corresponding to the flow passing through each edge
var int: max_flow;

constraint forall(i in 1..nAretes)(x[i] >= 0); %all flows must be positive
constraint forall(i in 1..nAretes)(x[i] <= u[i]); %all flows must be less than the capacity of the edge


constraint forall(i in 1..nNoeuds)
                 (sum(j in 1..nAretes where A[j,2] == i)
                   (x[j]) - sum(j in 1..nAretes where A[j,1] == i)
                     (x[j]) == 0);%out = in
                          

constraint max_flow = sum(i in 1..nAretes)(c[i] * x[i]);  %objective
                   
                                     
solve maximize max_flow;