How believable is the play The Bear?

The play The Bear is pretty unbelievable, when you really think about it. Here is a man who is owed money, a woman who has locked herself up in her house because her cheating husband died, and they go from hate to love in a total of about ten minutes.

Smirnov comes to the house angry. He is a businessman owed money from pretty much everyone, and he owes money to the bank. So he goes from customer to customer demanding his money, and each has a more ridiculous reason for not paying him. He comes to Popova, who is in herself a pretty ridiculous character. After her husband's death, she finds out he has been cheating on her, so to prove to him what real love is, she locks herself in her house, refusing to come out for anyone.

Is this realistic? Parts of it are, of course. But the chairs all break under Smirnov, her servant is a bit outrageous, and then there's the whole idea of the duel. Smirnov is so enraged that he decides to duel Popova, a woman, and she accepts, then asks how to shoot a gun. Would someone get into a duel who never shot a gun? Of course not.

Then there's the fact that they fall in love, which is pretty ridiculous as well. Smirnov goes from wanting to kill this woman to love in about a minute, and she eventually accepts his love.

In short, the play is a farce.