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IELM_assignment_1

# IELM_assignment_1 - IEEM 202 Assignment#1 Due date 21...

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IEEM 202, Assignment #1 Due date: 21 September 2005, Wednesday, 12:00 noon. Question 1 (30 marks) : For the blending problem discussed in class: The problem is to determine the optimal amounts of three ingredients to include in an animal feed mix. The final product must satisfy several nutrient requirements. The possible ingredient, their nutrient contents (as a proportion of the ingredient), and the unit cost are shown in the table Ingredient Calcium Protein Fiber Unit cost (cents/kg) Limestone 0.38 0.0 0.0 10.0 Corn 0.001 0.09 0.02 30.5 Soybean meal 0.002 0.50 0.08 90.0 The mixture must meet the following restrictions. Calcium: at least 0.8% but not more than 1.2% Protein: at least 22% Fiber: at most 5% The problem is to find the composition of the feed mix that satisfies these constraints while minimize cost. The model is: Variable Definition L,C,S: proportion of limestone, corn, and soybean meal, respectively, in the mixture Objective Function: Minimize Z = 10L + 30.5C + 90S Constraints: Minimum calcium: 0.38L+ 0.001C+ 0.002S>= 0.008 Maximum calcium: 0.38L+ 0.001C+ 0.002S>= 0.012 Minimum protein: 0.09C+ 0.50S>= 0.22 Maximum fiber: 0.02C+ 0.08S>= 0.05 Conservation: L+ C+ S= 1 Non-negativity: L,C,S >= 0

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IELM_assignment_1 - IEEM 202 Assignment#1 Due date 21...

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