Where are you reading 1 cent/month? The cheapest way I can see to run a small app+db project on Heroku now is to use an Eco dyno at $5/month with a Mini Postgres instance at $5/month, for a total of $10/month.
If you don't want your project to sleep, you probably want a Basic dyno ($7/month) instead of an Eco dyno.
Am I missing something?
Edit: I meant to add a link to the pricing page.
https://www.heroku.com/pricing
