Let G = (V, E) be a directed graph, and let wv be the weight of vertex v for every v ∈ V . We say that a directed edge e = (u, v) is d-covered by a multi-set (a set that can contain elements more than one time) of vertices S if either u is in S at least once, or v is in S at least twice. The weight of a multi-set of vertices S is the sum of the weights of the vertices (where vertices that appear more than once, appear in the sum more than once). 1. Write an IP that finds the multi-set S that d-cover all edges, and minimizes the weight. 2. Write an LP that relaxes the IP. 3. Describe a rounding scheme that guarantees a 2-approximation to the best multi-set

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