Blending problem A manufacturer produces a feeding mix for dairy cattle. The feed mix contains two active ingredients and a filler to provide bulk. One kg of feed mix must contain a minimum quantity of each of four nutrients as below: Nutrient A B C D gram 80 50 25 5 The ingredients have the following nutrient values and cost A B C D Cost/kg Ingredient 1 (gram/kg) 100 50 40 10 40 Ingredient 2 (gram/kg) 200 150 10 - 60 What should be the amounts of active ingredients and filler in one kg of feed mix? solution is x1= 0.5905, x2=0.1364 and x3=0.2727. #######################################3 ### COMPONENT pIngredient1 ! Part ingredient 1 pIngredient2 ! Part ingredient 2 pFiller ! Part ingredient 3 = filler ### END COMPONENTS ### PARAMETERS ! Minimum Nutrient composition MinNutrientA = 80 MinNutrientB = 50 MinNutrientC = 25 MinNutrientD = 5 ### END PARAMETERS ### INEQUALITIES NutrientA : 100*pIngredient1 + 200*pIngredient2 > MinNutrientA NutrientB : 50*pIngredient1 + 150*pIngredient2 > MinNutrientB NutrientC : 40*pIngredient1 + 10*pIngredient2 > MinNutrientC NutrientD : 10*pIngredient1 > MinNutrientD ### END INEQUALITIES ### EQUALITIES Balance : pIngredient1 + pIngredient2 + pFiller = 1 ### END EQUALITIES ### COST 40 * pIngredient1 + 60*pIngredient2 ### END COST