can someone explain the "job offer" puzzle

[anon]

It's a decision making problem I read about in school some years ago: you are trying to decide which job offer (out of many) you should accept. You only get one offer at a time and if you turn it down it's no longer available, but if you accept it you can not accept any other offers which might turn out to be better.

 

I don't have my notes anymore and I've only found the following document online: http://www.cs.princeton.edu/courses/archive/fall99/cs341/handouts/k2.pdf In that handout the answer seems to be k, but it's not clear to me what the optimal approach is, especially if n is not fixed. Can anyone please explain? If there is an optimal solution then maybe it has some relevance in real life situations too.