harry potter - How does Azkaban's management work?

I was under the impression that only Dementors are guarding the prison of Azkaban and are only there to keep the inmates on their cells, though after reading again the following passage it put me into thoughts:

'One night, when (the Dementors) opened my door to bring food, I slipped past them as a dog. It's so much harder for them to sense animal emotions that they were confused ... I was thin enough to slip through the bars. I swam as a dog back to the mainland. I journeyed north and slipped into the Hogwarts grounds as a dog. I've been living in the Forest ever since.'

Prisoner of Azkaban; chapter 'The Servant of Lord Voldemort'

So Sirius says that he escaped from his cell when the Dementors brought him food.... I say what??? Dementors dont obey anyone, not even the commands of the Ministry of Magic.

So the actual question is, How is the Azkaban prison managed? e.g. who cooks the food? the inmates have blankets, who is washing these blankets etc etc

Answer

The Dementors manage Azkaban

We know that after Azkaban was established, the atmosphere therein was so terrible that even brief visits were next to unbearable:

They turned a blind eye to the inhumane conditions inside the fortress, permitted it to be magically enlarged and expanded and rarely visited, due to the awful effects of entering a building populated by thousands of Dementors.

It seems very unlikely, then, that any witch or wizard could work there, if the mere incidental effects of visiting were so terrible.

As such, the Dementors must take on the routine duties of "caring" for prisoners, such as providing them with food and protection from the elements. This might seem incongruous, given that the general interest of Dementors is solely in draining the emotions from anyone, but it is not so; if the Dementors keep their victims alive, they can feed on them for decades, whereas without providing food and water, the Dementors could only feed for weeks. The Dementors are of roughly human intelligence; they can follow such a strategy as long as they are not too hungry.

Your own quote indicates that Dementors bring food to prisoners. They can also bring blankets and so forth, so long as they have a source of such things.

It does seem likely that food is transported from the mainland, nonetheless. (As indeed other essentials may be). A rocky island in the middle of a freezing ocean is a poor location in which to grow crops, and one wonders whether the Dementors would be particularly inclined to do so in any case.

One more thing to keep in mind is that Azkaban is terribly inhumane. No one needs to cook food. Just drop off some bread and water and the Dementors can give it to the prisoners. Clean blankets? The prisoners will be lucky if they ever get a replacement, or perhaps even a blanket at all.