Statement 1:
Given a graph $G=(V,E)$ in which each vertex $v \in V$ has an associated positive weight $w(v)$, we can use linear programming to find the lower bound on the weight of the minimum-weight vertex cover.

Statement 2:
The lower bound can be found by maximizing the following

$ \sum_{v \in V} w(v)x(v) $

subject to

$ x(u)+x(v) \ge 1 $ for each $(u,v) \in E$

$ x(v) \le 1 $ for each $v \in V$

$ x(v) \ge 0 $ for each $v \in V$

In the light of the above statements, choose the most appropriate answer from the options given below: