Recurring plumbing issues – why not fixed?

I began renting an apartment in a large complex beginning on July 5th this year. Since moving in, I have had several recurring problems with my kitchen. First, my dishwasher stops cleaning dishes properly. Then, my sink begins to back up. If I try to run my garbage disposal to clear the drain, all I get is a "buzzing" noise, and no action from the blades. Quickly, the sink becomes clogged completely and I can no longer wash my dishes, even by hand. Now, I have 2 roommates, who have partial custody of a 2 year old. We produce a lot of dishes. If this happens on a Friday, I sometimes have to wait 3 days before they will come "repair" the problem. In this time, dishes pile up and the sink smells. It’s pretty disgusting and unsanitary, really.

This exact issue has taken place at least 6 times since we moved in back in July. The complex is owned by a large rental company, and I am finding it difficult to understand what the actual problem is, and why its so impossible to fix. I’ve had garbage disposals and dishwashers all my life, but I keep getting told that I should just "not put so much food in there", which is ridiculous. I am aware of how to operate these things. Isn’t 6 or more incidents in just under 3 months a little bit ridiculous? The dishwasher and the disposal aren’t necessities (though they are a part of why we chose to rent this particular apartment), but the sink?! I would think I should at least be able to hand wash things, or run water down it.

Any advice or similar experiences? I don’t know what I need to do in order for them to actually FIX this issue, and not just put a bandaid over it for another couple of weeks.

Thanks!