Objectivism

Are there any objectivists out there? Danny? Anyone? Because I have a question. If I understand objectivism correctly, the basic premise is that you should not live for others. Instead, you should do what is in your self interest.

The common objection to this is, what if an objectivist sees someone drowning? Acting only in their narrow self interest, they would let the person drowned. But objectivists always respond, that self interest should not be construed so narrowly, or that's not a proper understanding of self interest. That's fair enough. I mean, it's arguably in a person's self interest to save another. It would create a relationship. Or it might impress others.

So here's the hypothetical I have. Suppose an objectivist happens upon a drowning person he doesn't know. He has no reason to believe that he wants to know them. Or maybe it's someone he dislikes. There's no one else around. All he has to do is throw a life vest at the person to save him. Can an objectivist decide not to? If not why not?