An indefinite and somewhat large number; more than a few. Example: We watched quite a few of the World Cup matches on TV.
A person can not fuction as managing director of a large number of companies. One can be director in quite a few companies. Even many is also indicative of large number. The proper is; He is the managing director of a few companies.
In the sentence, "of" is appropriate because, it is intended to finance working capital needs of producers,( working capital needs possessed/belonging to producers) You can say: to finance working capital needs for production. (For the purpose of production)
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