MTI very helpfully lists the complete orchestration for its shows on their respective information pages within the site.
Here's the breakdown for
West Side Story:
http://www.mtishows.com/show_detail.asp?showid=000077 The full orchestration is for 28 players, and the alternate scoring is for 19. Keep in mind that MTI offers rentals of what it calls OrchExtra, which can fill in missing parts when you don't have players to cover every single part.
As has already been mentioned, however, this show has the reputation - even among professional musicians - of having one of the most difficult orchestral accompaniments to play among all stage musicals. One group in my town used to stage a musical every summer with local teenagers, using a teenaged orchestra. For
West Side Story, they chose to hire members of our local symphony orchestra instead.
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Jeff Grove
Theatre Teacher, Aesthetics Department Chair
Stanton College Preparatory School
Jacksonville FL