How much IP do you get for winning & losing games in the various modes/maps?

My understanding is that you get a base number of Influence Points (IP) for losing each game and a little more for winning a game. In addition, the amount of time a games goes on seems to factor into the calculation as well. For the following modes, what is the base IP gain for wins and losses of the various game lengths? If there's a predictable calculation for IP per minute for wins/losses, that would be an acceptable answer.

I'm not interested in calculations including IP bonuses for your first game, bonuses for streaks of games where you didn't leave, or any other bonuses.

• PvP
  • Twisted Treeline (3v3)
  • Summoner's Rift (5v5)
• Co-op vs. AI
  • Beginner, Summoner's Rift (5v5)
  • Intermediate, Summoner's Rift (5v5)
• Custom
  • Twisted Treeline (3v3)
  • Summoner's Rift (5v5)

Bonus points if you take the initiative to calculate the optimal game length for IP gain. By that, I mean "at what point does ending the current game one way or the other and being able to start a new game result in more IP gain over the course of a play session than if the current game continued".