In this country, large amounts of the population are slaves. About 1 in 5. Most are used in construction projects, like building walls and aqueducts. These slaves have 14 hour construction shifts, with 2 hours of mealtimes and 8 hours of sleep. At mealtimes, they are given the same three foods, potatoes beans and kale, mashed up with a glass of water to wash it down, and get sold meat and alcohol every last day of the month. My question is, could they survive on this diet alone, or would they need to add an something extra to their food?
One of the reasons that humans are so successful as evolutionary products is that we're generalists. Compared to other animals, we can live in almost any environment, eat almost anything and even adapt tools (like shoes) to do the things our bodies aren't adapted to yet.
The leg and foot are perfect examples of this. We can run reasonably fast, climb well, swim in the water, kick our enemies, etc. We have running shoes, hiking boots, fins (they're not called flippers) for swimming, etc. BUT; we can't run faster than (say) a horse, climb better than a goat, or swim faster than a dolphin. We're generalists.
When it comes to food, we can eat almost anything. The amount of salt the average human eats would kill a cat. The list of foods we eat that dogs can't (chocolate, avocadoes, etc.) is huge. We're also omnivorous, meaning that we can eat both meat and plants. BUT, we can't eat all meat. Dog livers for instance would kill us with concentrations of Vitamin A. We also can't eat all plants; grass and other high cellulose foods we can't digest. (Ironically, it's that inability that makes domestication of animals easier; we're not competing for the same food as them.)
That said, everything evolution produces comes with a price. In our case, that price is a wider nutritional requirement. We actually HAVE to eat a wider variety of food to get all the essential nutrients a body needs. Ideally, that just means eating a wide variety of foods and you're generally good, but there has been some research on how to lower the diversity of food intake and still maintain health over a long term.
Vegetarians and Vegans for example can't just cut meat out of their diet and keep going with their existing diet and stay healthy. They have to 'replace' meat with something. Usually, that means a higher reliance on mushrooms and nuts for protein and fats, and a lot more green leafy vegetables like spinach for iron, etc.
There are some 'superfoods' that have a large supply of nutrients (like almonds and kale) and there are also some foods that are almost nutritionally complete, like eggs and potatoes. The problem with both these foods is that the proportion of nutrients is wrong; potatoes for instance would give you around 2.5 to 3 times your energy requirement before most of your nutritional needs were met. For workers or slaves, that may not be so bad a thing on the surface but your slaves are definitely going to need heavy protein and calcium in their diet as well for muscle and bone development.
So; could your slaves survive on the diet you describe? Not enough water, but other than that, possibly. Could they remain healthy enough to work hard for you on that diet? Not even close.
Slaves and food are a classic example of Capital Expense v. Operational Expense (CapEx v OpEx) decision making, and it ultimately comes down to which type of expenditure is easier for you to maintain. If slaves are expensive, then you want to maintain your capital (the slaves) with high quality food (high OpEx) because putting more money into maintenance is still cheaper than buying more slaves. If slaves are cheap, you don't bother with high OpEx because your CapEx in replacing your slaves is cheaper.
My Grandfather (and yours too no doubt) spent a LOT of time polishing his boots. He checked the boots of men coming around looking for work as a sign of that man's character. Why? Because boots were expensive, and looking after them showed that you were conscientious in caring for what you owned, and by extension you'd care for your job as well.
Today, boots cost far less and while we maintain them, we don't spend the time on them we used to because at their current cost (as a percentage of income) they're more or less expendable. We spend that time washing our car or cleaning out the gutters of our house instead, because those assets still cost a lot and therefore need to be maintained.
In that sense, this question only becomes relevant as an efficiency issue and THAT would only be the case if you have a serious shortfall in OpEx funds AND CapEx funds. If that's the case, you will be able to restrict the diet a little, but not to the extremes you've asked about if you still want your slaves to be capable of working.
In all other cases, feed your slaves well. Even modern research doesn't tell us everything about the human nutritional needs and the best mitigation of risk to human health is still a varied diet.