3. A town has r residents R1, R2,.., Rri q clubs Ci, C2,.. ,Cq; and p political parties 11,, , P,. Each resident is a member of at least one club and can belong to exactly one political party. Each club must nominate one of its members to represent it on the town's gov- erning council. However, the number of council members belonging to the political party Pk is at most uk. The normination problem is to find a council that satisfies this "balancing" property or to show that such council cannot be formed. Formulate this problem as a maximum flow