Length : around 10 minutes
« An animal feed company produces concentrates for cattle using various types of ingredients : protein crops (peas), cereal (maize) and cattle cake (soya-bean).
The concentrates obtained must have a minimum guaranteed content of TNM (Total Nitrogenous Matter) and fat as well as maximum mineral matter and crude fibre contents
| Minimum contents | TNM (g/kg) | Fat (g/kg) |
| Concentrate | 200 | 25 |
| Maximum contents | Mineral matter (g/kg) | Crude fibre (g/kg) |
| Concentrate | 70 | 65 |
The content of each of these components is known for every ingredient.
| Contents | TNM (g/kg) | Fat (g/kg) | Mineral Matter (g/kg) | Crude fibre (g/kg) |
| Maize | 81 | 37 | 12 | 22 |
| Peas | 207 | 10 | 30 | 52 |
| Soya-bean cakes | 453 | 19 | 64 | 60 |
The cost of maize is 148€/T, that of peas 195€/T and soya-bean cakes 355€/T. »
Source : P. Haurez, Utilisation des protéagineux dans l’alimentation des bovins viande, synthèse réalisée par l’Institut de l’Elevage, 2002.
It is possible to develop a linear programming model which helps determine the optimal formulation of a kilo of concentrate so as to respect the guaranteed contents while minimizing production costs.
Consider the linear programme and answer the questions.
Let C be the cost of concentrates (euros)
M the amount of maize used in a kg of concentrate (in kg)
P the amount of peas used in a kg of concentrate (in kg)
T the amount of soya-bean cakes used in a kg of concentrate (in kg)
