Romans in later times had fully developed armament factories owned by private corporations that were contracted by government to make cheap, good quality and easily reproducible swords. Just like today.
Dunno about hellenistic cultures, but they probably had some sort of smaller scale factories too.
@ MeinPanzer: On the axes, you should search Attic pottery for Persian representations. You'll find that they are either using a Greek kopis, an Akinakes or....surprise, surprise, an axe.
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