= Solution
Fix a primal <feasible point> $x_0$. For every dual <feasible point> $y$, nonnegativity and the primal and dual inequalities give
$$
c^Tx_0\leq x_0^TA^Ty=y^TAx_0\leq y^Tb.
$$
Hence \b[the dual objective is bounded below by $c^Tx_0$ wherever it is feasible], which is <weak duality>. This is the meaning of “bounded” in this assertion; it does not say that the dual feasible set is bounded, or that it is nonempty. For example, with $A=0$, $b=0$, $c=1$ and a single variable, the primal is feasible and unbounded above, while its dual would require $0\geq1$ and is infeasible.
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