I am preparing for a talk on "Approximation Algorithms", aimed at undergraduate students. In order to motivate the topic, I want to give them an example of a problem which is easy to describe and has a ridiculously easy approximation algorithm. But the question - "Whether one can one can do better?" must be still open for that problem.
In short, what is a simple-to-describe problem whose approximation ratio is still open?
EDIT: Finding minimum Vertex Cover of a simple graph $G(V,E)$ happens to have a simple algorithm with approximation ratio 2. But its approximation ratio is still an open question.