Looking at the pefsu problem of the Moscow Mathematical Papyrus here I don't understand why the algorithm takes 1/2 of the calculated grain measure to produce beer. Why aren't the 5 heqats multiplied by 4 to get 20 quantities of beer which would be a better deal in exchange?
The problem transcribed:
Example of calculating $100$ loaves of bread of pefsu $20$
If someone says to you: "You have $100$ loaves of bread of pefsu $20$
to be exchanged for beer of pefsu $4$
like $1/2$ $1/4$ malt-date beer"
First calculate the grain required for the $100$ loaves of the bread of pefsu $20$
The result is $5$ heqat. Then reckon what you need for a des-jug of beer like the beer called $1/2$ $1/4$ malt-date beer
The result is $1/2$ of the heqat measure needed for des-jug of beer made from Upper-Egyptian grain.
Calculate $1/2$ of $5$ heqat, the result will be $2$ $1/2$
Take this $2$ $1/2$ four times
The result is $10$. Then you say to him:
"Behold! The beer quantity is found to be correct."
My interpretation is that "a des-jug of beer like the beer called 1/2 1/4 malt-date beer" just requires half the grain than beer made from Upper-Egyptian grain. I know basically nothing about making beer, but could be because the grain required is more valuable, or somehow the process to make 1/2 1/4 malt-date beer uses other ingredients or something.