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Restricted version of vertex cover

Suppose we have a $(A,B,E)$ bipartite graph and a positive integer k. Suppose that k is smaller than $|A|$ and we want to find one of those k element subsets of $A$ which covers the most points from $B$. I can only come up wirh exponential algorithms. Is this in $P$?

Also is mixed integer programming for maximal flows in $P$? It can be easily formulated as such.

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