Balancing rations using computer Formulating least cost rations –The most commonly used computer programming technique to do this is called linear programming (LP) –The program contains equations to predict animal requirements and supply of nutrients needed to meet requirements –On the amounts of nutrients such as energy, protein, etc. minimum and maximum limits can be used. –We also can set minimum and maximum constraints on the amount of ingredients like rapeseed meal, barley, wheat etc. –Set the objective function, which is in this case a linear equation with which the linear programming minimizes the price of the ration –Then the computer finds the optimum combination of feeds that provides the nutrients that meets the constraint set. –The optimized diet should be re-evaluated if needed

The mathematical model of linear programming linear matrix: a 11 X 1 + a 12 X 2 + …..a 1n X n r 1 a 21 X 1 + a 22 X 2 + …..a 2n X n r 2 a 31 X 1 + a 32 X 2 + …..a 3n X n r a m1 X 1 + a m2 X 2 + …..a mn X n r m the objective function: P 1 X 1 + P 2 X 2 + P 3 X 3 + …. P n X n = MIN or MAX where: X 1 + X 2 + X 3 … = the ratio of feedstuffs a 11 - a mn = coefficients (energy, protein, Ca, P etc. contents of feedstuffs) r 1 - r m = constraints (requirement values like energy, protein etc.) = relations P = the value of the objective function (in this case the minimum price of the ration) P 1 - P n = the prices of feedstuffs

Requirement values are the nutrient contents of the compound diets growing diet for broiler chicks AMEn = 13,38 MJ/kg (min) Crude protein = 200 g/kg (min) Crude fibre = 40 g/kg (max) Ca = 9 g/kg (min) available P = 3,5 g/kg (min) Lysine = 10 g/kg (min) Methionine = 3,8 g/kg (min) Methionine + cystine = 7,2 g/kg (min)

AMEn MJ/kg C. prot. g/kg. C. fibre g/kg Ca g/kg avail. P g/kg LYS g/kg MET g/kg M+C g/kg Price Ft/kg corn14, ,21,12,61,73,632 animal fat29, extr. soybean meal (44%) 9, ,92,128,36,113,160 meat meal8, ,440,330,78,014,068 L-LYS DL MET limestone Hostaphos Feedstuff table