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I'm struggling to put together a formula that would estimate the amount and cost of frying oil to fry, say, chicken. Let me define some variables:

  • a - cost of oil per liter
  • b - number of times the oil can be reused without compromising quality of food
  • c - percentage (expressed as a decimal) of per unit of oil required to fry per unit of chicken (e.g. 1 liter of oil can cook 1 kilogram of chicken = 1)
  • d - maximum capacity of the deep fryer, in liters. Assume fryer will always be filled to maximum.
  • e - total weight of chicken to fry, in kilograms

I'm not sure if I'm missing any variables, but here are my questions:

  1. What's the formula to compute the amount of oil for a given e?
  2. What's the formula to compute the cost of the oil for a given e?

EXAMPLE: If I had 4.5 kilos of chicken to fry, and that the deep fryer can hold 2 liters of oil, and that the oil can be reused 5 time, and say that I need a liter of oil to fry a kilo of chicken. This means:

  • I can cook 2 kilos of chicken at a time. I will need to cook 3 separate times to cook 4.5 kilos. So, 4.5 raised to the nearest 2 (oil capacity) = 6 / 2 (oil capacity) = 3 (times).
  • Since the 2 liters of oil can be used up to 5 times, it means that my 3 times cooking is still within range of safe cooking. I would only need 2 liters of oil (but need to do 3 batches of chicken)
  • If a liter of oil is 5 dollars, then 2 liters = 10 dollars. And I used 3 times out of the 5 times the oil can be used, that means my oil cost is 6 dollars.
  • Summary: I need 2 liters of oil to cook 4.5 kilos of chicken in 3 batches at the cost of 6 dollars.

How do I express this in a formula so I can plug in whatever values I need?

NOTE: I guess I'm assuming that if a fryer has a 1 liter oil capacity that I can put in that amount of oil AND also put in 1 kilo of chicken. I'm not sure if that assumption is correct.

COST OF OIL SOLUTION:

$$\frac{d \lceil \frac{ce}{d} \rceil}{bd} ad$$

AMOUNT OF OIL SOLUTION:

$$\lceil\frac{\lceil \frac{ce}{d} \rceil}{b}\rceil d$$

MathNewbie
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  • What is the density of a chicken? The chicken will displace some volume of oil. – Q the Platypus Aug 18 '17 at 04:10
  • Let's not factor that is (so the NOTE I added at the bottom). Perhaps the variable d can factor that in (meaning, it's the maximum oil the fryer can hold and still allow the amount of chicken it needs to fry). – MathNewbie Aug 18 '17 at 04:34
  • Are you accounting for the amount of oil absorbed by the chicken? I think that will depend on the amount of surface area of the chicken. The frying process displaces water at the surface with oil. – Joel Aug 18 '17 at 05:13
  • No. It doesn't need to be 100% accurate. A good enough estimate will suffice. Just trying to make reasonable guestimate of oil cost. – MathNewbie Aug 18 '17 at 05:20

2 Answers2

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If the fryer must be filled for each batch, the amount of oil needed will be $⌈⌈ce/d⌉/b⌉\cdot d$ ....... $⌈ce/d⌉$ represents the 3 batches of cooking in your situation. $⌈⌈ce/d⌉/b⌉\cdot d$ means that if the number of batches exceeds $b$, then more d liters of oil must be added.

Xiangyu Chen
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Assuming that the chicken has no volume and won't displace any oil, and c liters of oil are needed to fry 1 kg of chicken, the amount of oil needed in liters will be ce/b, and the total cost will just be ace/b. As long as the oil is enough to fry all chicken without being overused, the value of d is irrelevant(must >0). If you want the fryer to be filled to the top every time, as your example indicates, it would be much more complicated to find the minimum oil needed. And the oil would spill out after being heated.

Xiangyu Chen
  • 644
  • You're right about d bring irrelevant. I'm studying your answer and will try to plug in some actual numbers. I assumed that a ceiling function would be needed. – MathNewbie Aug 18 '17 at 05:22
  • Assume maximum oil capacity + displacement caused by chicken does not cause oil to over spill. – MathNewbie Aug 18 '17 at 05:38
  • Say you put 2 liters oil and one kg chicken. Would the extra liter count as unused? – Xiangyu Chen Aug 18 '17 at 05:45
  • No. It's used. In my example, say there was 4.5 kg of chicken, we would cook 3 times. 2 kilos of chicken in 2 liters of oil the first time, then another 2 kilos of chicken in 2 liters of the same oil the second time, and finally the remaining .5 kilos of chicken in the same 2 liters of oil. – MathNewbie Aug 18 '17 at 05:48
  • This would count at 3 uses of the oil. It'll only be usable for another 3 times. – MathNewbie Aug 18 '17 at 05:49