What kind of employees work at Devlin Whitehorn's Nimbus Racing Broom Company? Does Whitehorn use house elves, hire Witches & Wizards, or employ someother means to charm his products? Who makes the brooms?
I believe it must be wizards. House-elves have some magic but it's not the same as wizards', and goblins can give crafted items special properties but I doubt any would have interest in mass-producing broomsticks. Further, brooms are stated to have several named charms (cushioning, braking), and we've only ever seen named charms produced by wand-carriers; house-elves and goblins just do what they do without needing words (and it doesn't seem the same as nonverbal spells). So at least the magic of broomsticks is almost certainly created by wizards, including for the Nimbus company. And the spells are likely a trade secret, otherwise any decent wizard could make his own broomstick, so I wouldn't be surprised if the company owner himself put the important enchantments on each broomstick.
The closest we get to an explicit canon answer for this question is in Quidditch Through the Ages:
Nevertheless, nineteenth-century broomsticks were generally incapable of achieving high speeds and were often difficult to control at high altitudes. Brooms tended to be hand-produced by individual broom-makers, and while they are admirable from the point of view of styling and craftsmanship, their performance rarely matched up to their handsome appearance.
This is written in the past tense, implying something has changed, but from the rest of the chapter I gather that "something" is "individual", not "hand-produced".
The breakthrough occurred in 1926, when the brothers Bob, Bill, and Barnaby Ollerton started the Cleansweep Broom Company. Their first model, the Cleansweep One, was produced in numbers never seen before and marketed as a racing broom specifically designed for sporting use.
There was no mention of any broomstick company before this, and by founding a company together, the three of them could create broomsticks faster than any of them individually, in an assembly-line fashion.