MA.7:5.2 - Reconstruct the comparison when product mix changes
Suppose the original 100 units comprised fifty A requiring one material unit each and fifty B requiring three. Their reference requirement was 50 × 1 + 50 × 3 = 200 materials. Actual output is thirty A and ninety B. Under unchanged requirements within each product, those outputs require 30 × 1 + 90 × 3 = 300 materials.
The planned and actual totals are still 600 and 1,200, but the intermediate accounts now expose a different explanation:
| Account | Material quantity | Price | Cost | Difference from preceding account |
|---|---|---|---|---|
| Planned 50 A and 50 B | 200 | 3 | 600 | — |
| Actual volume 120 at original 50:50 mix: 60 A and 60 B | 240 | 3 | 720 | 120 volume |
| Actual mix: 30 A and 90 B, at reference requirements | 300 | 3 | 900 | 180 mix |
| Actual material consumption | 300 | 3 | 900 | 0 within-product usage |
| Actual price | 300 | 4 | 1,200 | 300 price |
Thus 120 + 180 + 0 + 300 = 600. The earlier 180 aggregate usage component is now replaced by 180 mix plus zero within-product usage. Adding a further 180 mix to the old decomposition would double count it. The aggregate average rose from two to 2.5 because the output composition changed; this account supplies no evidence of increased waste.
Now change actual consumption to 324 materials on that same actual mix. At the reference price, consumption costs 972, so usage contributes 972 − 900 = 72. Actual price gives 1,296 and a price component of 324. The total difference is 1,296 − 600 = 696, reconciled as 120 volume + 180 mix + 72 usage + 324 price. Investigate the additional twenty-four materials through the operating records and competing explanations; their arithmetic cost does not establish a defect or assign responsibility.
If evidence supports a persistent move toward product B, MA.5 can update the future composition and its resource consequences. The earlier forecast remains available for learning. A different decomposition order can move interaction amounts between components, while the total and the need for causal evidence remain.