Two pens share one feed store but need opposite rations. Lactating dairy cows (left, cream) respond best to a protein-rich ration (~17% CP) at moderate-high energy; finishing beef cattle (right, red-brown) respond best to a lower-protein, energy-dense ration (~12.5% CP, grain-heavy). Each animal's output efficiency follows a bell curve around its type's nutritional optimum, so pushing the shared ration toward one animal's ideal pulls it away from the other's — the same tension a mixed-species farm faces when it can't run two separate feed lines.
efficiency = exp(−(protein−opt_p)²/2σp²) · exp(−(energy−opt_e)²/2σe²)
output = base_rate · efficiency FCR = daily feed intake / daily output
- Herd size — total animals across both pens; capacity is shared, so a bigger herd just fills both pens more densely.
- Herd mix — the balance of dairy vs. beef animals on the farm; shifts which pen is fuller without changing either ration.
- Crude protein — the ration's protein content; dairy cows need more of it to sustain milk synthesis than growing/finishing beef cattle do.
- Energy density — Mcal of net energy per kg of dry matter; beef finishing rations run hotter (more grain, less fibre) than typical lactating dairy rations.
Real-world relevance: this is why real mixed farms formulate separate total-mixed rations per group rather than one ration for the whole operation — a single compromise ration leaves feed-conversion efficiency on the table for whichever group it wasn't built for.