Utterly Mad

 
But the point is moot, because have I mentioned YOU WOULDN'T HAVE ANY WAY OF KNOWING YOU WERE THE LAST PERSON ON EARTH ANYWAY!!! 

I'm pretty sure we would all give up searching after a few days. A few years, for the more persistent of us.

I sincerely hope that if this hypothetical last person on Earth becomes reality, the last human is a woman, as continuing the species would be much more simpler if so.