I've got an interesting graph-theory problem. I am given a tree $T$ with $n$ nodes and a set of edges. $T$ is, of course, undirected. Each edge has weight that indicates how many times (at least) it has to be visited. We are strolling from node to node using edges and the task is to find minimal number of needed steps to satisfy above conditions. I can start from any node.
For example, this tree (edge weight along edge):
we need $8$ steps to walk this tree. That are for example: $4\to5\to6\to5\to3\to5\to3\to2\to1$
I don't know how to approach this algorithm. Is it possible to find this optimal tour or can we find this minimal number not directly?