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I'm doing practice problems for an upcoming exam and I'm unsure if the following problem is NP-complete. If it is can you please give me a hint as to what problem I should reduce to it. I believe it's NP-Complete and maybe the knapsack problem can be reduced to it but I'm not sure.
WEIGHTED VERTEX COVER:
Input: A weighted graph $G$ with integer weight $Wv>1$ on each vertex $v$ and an integer $T$.
Question: Does $G$ have a vertex cover with total weight at most $T$?