Jammey

An agricultural mill produces a different meal for cattles, sheep and chicken by mixing the following raw ingredients: corn, limestone, soyabeans and fishmeal. This ingredients contain the following nutrients: vitamins, protein, calcium and crude fat in the following quantities: Nutrients k Ingredients: Vitamin Protein Calcium Crude fat Corn 8 10 6 8 Limestone 6 5 10 6 Soyabeans 10 12 6 6 Fish meals 4 18 6 9 Let aik= quantity of nutirnt k per kg of ingredient i CONSTRAINTS: The meal has contract for the following: Cattle= 10000 kg demand dj Sheep= 6000 kg Chicken= 8000kg There are limited availabilities of the raw ingredients: Corn= 6000kg Supply Si Limestone= 10000kg Soyabeans= 4000kg Fishmeal= 5000kg the different feeds have quality bound per kg Vitamin Protein Calcium Crude fat min max min max min max min max Cattle 6 - 6 - 7 - 4 8 Sheep 6 - 6 - 6 - 4 8 chicken 4 6 6 - 6 - 4 8 The above value represent bounds: Ljk and Ujk Cost per kg of ingredients is as follows: Corn = N20 Limestone= N12 Soyabeans= N24 Fishmeal= N12 Formulate problem has a linear programming whose solution yields desired feed production levels at minimum cost. DATA dj = demand for product j (kg) Si = supply of ingredient i (kg) Ljk = lower bound on number of nutrients of type k per kg of product j Ujk = Upper bound on number of nutrient of type k per kg of product j Ci = cost per kg of ingredient i aik = number of nutrients k per kg of ingredients i DECISION VARIABLES Xij = amount (kg) of ingredient i used in producing product j demand for product j (kg)