I'm just setting everything out as little baby steps.
Now that we've established that a rational mans ultimate value in life is life itself, we can delve into the rational cardinal values a man hold. 1. Reason, 2. Purpose, 3. Self Esteem. The corrosponding virtues of said values are, respectively, 1. Rationality, 2. Productiveness, 3. Pride.
From that we can easily in/deduce that productive work is the central purpose of a rational man’s life. Reason is the source, the precondition of his productive work—pride is the result.
So we have there that productive work is the purpose of ones life, and what is productive work if not living?