It doesn't seem that hard to solve to me either. It's solvable with basic linear programming.

    1. Add a variable for each node, and a variable for each output edge from stations.
    2. For each reservoir add equality constraints to the sum of incoming edges with the coefficients given in the problem.
    3. For each station add equality constraints between the weighted sum of its inputs (which is 1 for the root station) and its outputs (which are the variables we added).
    4. Add an out_edge >= 0 constraint for each output edge on stations to forbid illegal negative flows.
    5. Add a variable m which is constrained to be less than all the output station variables.
    6. Maximize m.