Energy. A hen eats to satisfy its metabolisable-energy (ME) need, using the form of the classic NRC poultry relation (coefficients rounded):
ME_req = W^0.75 (173 - 1.95 T) + 5.5 dW + 2.07 EM [kcal/hen/day]
intake FI = ME_req / ME_diet [g/hen/day]
W is body weight (kg), T air temperature (°C), dW weight change (g/day) and EM egg mass (g/day). Warmer air trims maintenance, so intake falls in heat and rises in winter.
Photoperiod. Lay potential follows a logistic curve in light hours, centred near 10.5 h and saturating by 14-16 h, times an age factor and a heat penalty above 28 °C. Only the steady-state level is modelled.
Protein and calcium. An egg is about 12.5 % protein (net use about 45 %); maintenance takes 1.4 g crude protein x W^0.75. A shell holds about 2.1 g calcium; about 55 % of dietary calcium is retained (less when panting in heat).
EM_E = (ME_in - maint) / 2.07
EM_P = (CP_in - 1.4 W^0.75) / 0.278
lay = min(potential, EM_E / eggWt, EM_P / eggWt)
shell soundness = min(1, ((0.55 Ca_in - 0.3) / 2.1) / lay)
Energy or protein can limit the number of eggs; calcium limits shell quality. The "Ration vs egg mass" curve sweeps the corn share of your ration and shows where the limiting factor switches from light/age to protein.
Efficiency and cost. FCR = feed eaten / egg mass laid. Cost per dozen = 12 x feed cost per hen-day / sellable eggs per hen-day. Prices are illustrative; only feed is costed.
Honest simplifications. Flock-average hens with small weight differences; no vitamins, phosphorus, amino acids or disease; hens do not pick favourite particles (real hens prefer grain, which unbalances the diet); eggs appear the day after the feed that made them. For learning, not husbandry advice. This 2D page shares its maths with the 3D page.