Multicommodity Demand Flow in a Tree

We consider requests for capacity in a given tree network T = (V,E) where each edge of the tree has some bounded capacity u sub e. Each request consists of an integer demand d, and a profit w sub e, which is obtained if the request is satisfied. The objective is to find a set of demands that can be feasibly routed in the tree and which provide a maximum profit, denoted by OPT.