As a scriba, you earn 6-7 denarii per period. Already cooked food cost $18 for 6 portions. So to buy finished food, you have to work for at least 3 periods out of 4. If you buy grain and cook it, it costs $10 for 6 portions. So you need to work only 2 periods, but it has to been cooked. However, you can offset this by utilizing your servants. Household servant can cook food for the entire villa. Work servant can earn small income at the warehouse ($12-$16 per day). Pit fighter can earn decent income if you bet on her and she wins (up to $40 per day, but it is very hard). Brothel servant can earn more than work servant, but needs libido training first. If you have a decent brothel servant, you don't have to work at all, she will cover all expenses ($20-$24 per day). If you complete a first quest for Livia, you will get a first farm basically for free, which will help with food too. You also have some food and money at the start.
This is to simulate the hard beginning of any business. It is very well doable in many ways, but you have to plan. I have tested it many times and I was able to always start the business with these conditions.
Hunger system is mentioned in a kitchen tutorial, that pops up when you first enter kitchen. It also describes how food works.
You need to have low/medium/high quality food in your inventory. Each person in your villa (you, Livia, servants, tutors, bulls...) eats 2 food items every day (if they haven't eaten day before, it's more). This can grow up very fast, if you don't have a good food management and you bring a lot of people in. You need to upgrade your kitchen, to cook food faster. Always have household servant or Cornelia to cook food for you. You can have farms to grow food, instead of buying it. The food is basically a limiter to how many people you can support in your house. It is a management game, after all.
Early game strategy is to have 1-2 servants in training (optimally one that can help with food, like household or farm servant) and develop farms as soon as possible. Later game strategy is to have 4-6 farms, farm servant to work on them, cook to cook food and other 2-3 servants in training with tutors.
Also, you need to raise in ranks, before bringing more people in. You cannot support a large household as a scribe. You need to be at least a quaestor.
