The siege of Carthage was the main event in the third Roman war. It went on from 149 B.C. to the spring of 146 B.C. According to Wikipedia the Carthaginians would have had about 410 000 citizens and 90 000 defenders.
How did the Carthaginians keep their population alive? It wasn't like everyone in the city was doing nothing either, as
The city managed to produce 300 swords, 500 spears, 140 shields and 1,000 projectiles for catapults every single day
according to Appian of Alexandria.
As the image above shows most of the peninsula would have been occupied by the Romans, so more then a little farming seems impossible.
So my question is twofold:
1) How did the Carthaginians manage to procure enough food to keep most of their population alive and working for three years and
2) How did they manage to get enough drinking water? (I know they had large cisterns to store water, but can that really have been enough for the whole population, Especially with large amounts of refugees from the countryside?)