Seriously, I'm assuming the same ad driven model that has made Facebook profitable would work for a professional network to.
I know I have personally clicked on ads that are related to my profession. I'm far, far more tolerant (even accepting) of B2B advertising than I am of B2C.
It's tricky though. They would have to be careful not to turn it into a pure marketing play. There would have to be safeguards against that.
The key is they would have to keep their eye on the main value proposition:
Becoming the number one way professionals connect with the idea, events, and people who can help them do their jobs better.