Tragicomedy: The King of Portmanteaux

After reading Death of a Salesman, I'm ready to crack down on some of these 'evaluation of drama' questions and get busy analyzing literature, so let's start with question number two...

#2. Is the play a tragedy or comedy, a melodrama or a farce? If a comedy, is it primarily romantic or satiric? Does it mingle aspects of these types of drama? How important to experiencing the drama is the audience's awareness of the classification of the play?

I would say that the play is a tragedy, because I can't really see it fitting perfectly into any of the other types.  It is not overly emotional or exaggerated, like a melodrama, or obnoxiously funny or entertaining as a farce would be.  The closest thing I could think of it being is a comedy, in the most Shakespearean of definitions, because there is a partially-happy ending for at least Biff.  Because the play mingles in both genres, I've settled on categorizing it as a tragicomedy, the ultimate classification.  As far as importance goes, though, knowing that the play fits into this category is of mediocre concern.  Sure, it's crucial for the audience to understand that Willy died an unchanged man due to a tragic flaw (tragedy), and that Biff learned a little bit about himself and who he is through the process (comedy), I still wouldn't call these lessons imperative.  Then again, this would probably be a pretty boring play to sit through if it weren't for the cultural/literary significance and all...