Firstly, I'm not a mathematics major and this is my first question here so please be gentle.
My attempt at a simple calculation of efficiency . . .
$\mathtt n$ = (# of cases of ingredients)
$\mathtt b$ = (target yield per case) = 17
$\mathtt x$ = (total actual yield)
$\mathtt f(x,n)$ = $\frac{x}{bn}$ = (overall efficiency)
The problematic scenario . . .
Normally, the above is true. However, consider the following:
$\mathtt n_1$ = 30
$\mathtt n_2$ = 100
$\mathtt x$ = 0
$\mathtt f(x,n_1)$ $\neq$ $\mathtt f(x,n_2)$
NOTE: The last statement above is not true. The results of those two functions are both zero. Keep reading.
Question
What I am trying to describe here is this: yielding no product from 100 cases is clearly worse than yielding no product from 30 cases, but my efficiency formula will show both as 0%.
It seems there is a fundamental flaw in my approach, but I'm not familiar with mathematics enough to know what it is. Any suggestions about how else I could go about this?