Independent stage ratios commute for the final product, but not for the middle budget. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
One order has a twenty-unit intermediate budget
The 4/5 stage first gives intermediate budget 20 and final budget 4.
25⋅54⋅51=4
The reversed order has a five-unit intermediate budget
The final budget is still 4, but the intermediate budget is only 5.