Basic strategy to mathematically insure the fasted time:
You have your light duration, light value, and light cost
to maximize profit, never buy a light that costs more than
light duration x light value
as any light within this range maximizes profit.
get all of the lights on ASAP!!! this means increasing light duration at a rate that is double that of increasing light value.
Once you have all of the lights on, keep the seconds above how many seconds are left before your lights turn off, and ride that to the 1mil! post times under this comment!
