Can a person survive off of a diet alternating daily between mayonnaise, honey, beer, and wine?
Suppose an individual has a device which can produce one of a number of liquids, each day in particular quantities:
Given these specific foods, drinks, and quantities could 4-5 people survive for extended periods of time? The group of people are extremely active (a highly physical occupation) and have a separate supply of ample fresh water. Assume that the people have no refrigeration for the purposes of storage, so spoiled goods would be useless to them.
I've looked into minimum requirements, and this post on Biology.StackExchange has shed some insight into the difficulty in finding those numbers. It seems to me like the main limiting factor would be the lack of protein. It looks like mayonnaise has some protein from egg yolk, but it is unclear if you could consume enough without running into severe issues with a fat-high diet. Another specific concern I was looking in to was the complete absence of fiber in the available foods. Does that limit the potential to survive off of the diet?
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You can't survive from the list of foods (mayonnaise, honey, beer, wine, oil and vinegar) in given amounts, because you can't get enough vitamin C.
If I define "survive" as to live 10 years and remain healthy, then, in your scenario, which requires some physical activity, the minimal requirements (which can be much lower than Recommended Dietary Allowances) for adults:
Calories: 3,000
Protein: 35 g (Metabolic Basis of Obesity)
Fat: 67 g (at least 20% of total calories) (Nutrition Journal, 2017)
Carbohydrates: zero (theoretically), which also means zero fiber (a meat diet study, 1930).
Water: 2-3 liters
Sodium: ~1 g sodium, I guess; the minimal requirement is lower (~200 mg), but with sweating you need more.
Vitamin C: 10 mg - the minimal amount to prevent deficiency (scurvy) (Office of Dietary Supplements)
Iron: 1.36 mg (fao.org, p.198)
A certain amount of vitamins and minerals (Recommended Dietary Allowances, NAP.edu): minimal survival amounts would be likely less than 50% RDA.
From the amount of foods you have, you can't survive, because the only source of vitamin C (1 kg of honey per person per day if they are 4 persons) would provide only 5 mg vitamin C and everyone needs at least 10 mg to avoid deficiency (scurvy).
From other foods you have, everyone would barely get minimal (not recommended) amounts of protein and other nutrients, even when grossly exaggerating with calorie intake (> 5,000 - 6,000 Calories/day).
Here are some calculations from already exaggerated amounts of foods (you have more available, but that's not realistic to consume):
250 g mayonnaise: 1,700 Calories, 2.5 g protein, 187 g fat, 0.5 mg iron, 50 mg potassium, zero vitamin C
1 kg (1/4 gallon) honey: 3,040 Calories, 3 g protein, 4 mg iron, 150 mg potassium, 5 mg vitamin C,
4 liters (1 gallon) of beer: 1,720 Calories, 18 g protein, 0.4 mg iron, 1 g potassium, zero vitamin C
1 liter (1/4 gallon) of red wine: 850 Calories, 1,3 g potassium, 4.6 mg iron, zero vitamin C
Oil and vinegar do not have significant amount of vitamins and minerals, so they do not help.
Spoiler: You could easily get enough vitamin C from a fruit juice and protein and most other nutrients from milk (it can last some time even without refrigerator). Think that infants can survive solely on milk for more than a year.
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