I don't know how to properly named this question but here it goes:
Let $x, c \in \Bbb{R}^n$, $b \in\Bbb{R}^m$, $A \in \Bbb{R}^{m \times n}$. Consider LP in the form:
min $\{c^tx : Ax = b, x \ge 0\}$
Let $N_c \subset \Bbb{R}^n$ be defined as a set of $\forall c \in \Bbb{R}^n $ for which the LP is solvable for fixed $A$ and $b$. Analogously define sets $N_b \subset \Bbb{R}^m$ and $N_A \subset \Bbb{R}^m \times \Bbb{R}^m \times...\Bbb{R}^m $.
Prove or contradict that:
a) $N_c$ is convex
b) $N_c$ is a convex cone pointed at $(0,0)$ or a linear subspace of $\Bbb{R}^n$
c) $N_A$ is convex
d) For $A \neq 0$, $N_b$ has only one or only two points.
How can I describe an element of $N_c$ so that I would be able to prove that this set is convex? How about the description of $A$?
Many thanks for help.