I was taught to solve this type of problem using linear programming. For Perl implementation, Math::MatrixSparse looks the most apt from that point of view.

Wikipedia has numerous entries under "amb" but they seem rather eclectic and none quite hit the spot ("Al-Aqsa Martyrs Brigades" in particular ;))

Update: the module has a Gauss-Seidel method that can perform the actual solution for the OP example.