polyhedra and extreme points

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I am stuck with solving this problem, does anybody has idea, how to solve it ?

Let $P$ and $Q$ be polyhedra in $\mathbb{R}^n$. Let $P +Q := \{x+y ~\vert~ x \in P; y \in Q \}$

a) Show that $P + Q$ is a polyhedron.

b) Show that every extreme point of $P + Q$ is the sum of an extreme point of $P$ and an extreme point of $Q$.