>(1+v) t_max = 75+exp(c1 t_max)
>Even if you live a perfectly "virtuous" life (v=0), you will die
>eventually if c1 is too small. In this case, we can assume c1 to be
>close to zero and the total pleasure over life P(t_max) = v * 76/(1+v),
>which increases with v - life fast and die young.
>But if c1 is large enough, then the above equation may lack a
>solution. That means that for sufficiently low v, you can life forever
>and the total pleasure over life will diverge. In fact, in this case
>the optimal strategy would be to first choose a v just large enough
>for the curve (1+v)*t to be tangent to 75+exp(c1 t), and after this
>point increase v exponentially. A more cautious person might chose a
>somewhat lower v.
May I postulate that Virtue does not equal one minus vice? A lot of people, for instance, drink and also exercise. And if we accept this postulate, then the equation is missing at least one variable which can radically alter the shape of the function. (I know you made the suggestion in jest, but let's extrapolate a bit.)
If an additional variable -- let's call it T, virtue of a sort not incompatible with vice, which itself extends life, however finitely -- is included, then c1 can be commensurately smaller, of V commensurately larger, at least for a while. (How might T manifest? Well, how about meditation, or yoga, or some of the so-called occult arts [any of which which may only be ways of activating certain circuits in our nervous systems that the existing scientific lexicon can't yet describe]?) And if T has an enduring benefit, so that at age 90 the practise of, say, meditation adds to one's lifespan as much as it does at age 70, then a smoke or two might be okay after all if you're willing to contemplate your navel as well.
This can become a can of worms of course. It's only a matter of degree between meditating and sacrificing chickens without empirical evidence that a particular practise does in fact extend life. But we hardly want for such evidence in some cases -- meditation, yoga, and some of the taoist arts immediately spring to mind.