Why do factories impose a minimum order quantity?

Almost always because set-up cost is fixed. Stopping a machine, cleaning it, fitting a mould or a screen, running first-off samples and getting to a stable process costs roughly the same whether the run is 50 units or 50,000, so a small run makes that fixed cost dominate the unit price. The other two drivers are material minimums — a mill may sell fabric or resin only in full rolls or drums, and the factory inherits that floor — and capacity priority, where a busy factory prices small runs high on purpose so they do not displace large ones. This is why the effective way to lower an MOQ is to pay the set-up separately, accept a stock colour or material, or accept a deliberately higher unit price for a trial run.