I heard the guy who write the Unofficial Guide say that it depends on the type of resort you're staying at. For a deluxe it's about 5/6 nights. For a moderate it's 10/11, and for a value it's about 14...I think.
I know mousesavers.com has a page dedicated to the specific details of the currently available discounts for AP holders. You should be able to get a reliable, accurate answer using math for yourself from the numbers listed there.
I would recommend not taking the food discount into consideration in your first round of math to check and see what's worth it. Then add in the expected food discount numbers.
Either way, only one AP is needed per room rented, which you probably already know.