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IELM_assignment_1_solution

# IELM_assignment_1_solution - IEEM 202 Assignment#1 Solution...

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IEEM 202, Assignment #1 Solution Due date: 21 September 2005, Wednesday, 12:00 noon. Question 1 (30 marks) : For the blending problem: 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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The result report is shown as below: Number Name Value Status Reduced cost Objective coefficient Range lower limit Range upper limit 1 L 0.03 Basic 0 10.0 -- 17.44 2 C 0.65 Basic 0 30.5 24.40 90.21 3 S 0.32 Basic 0 90.0 30.45 123.89 The constraint analysis report is shown as below: Number Name Value Status Shadow price Constraint limit Range lower limit Range upper limit 1 Calcium 0.01 Upper -19.62 0.01 0.0080 0.2137 2 Protein 0.22 Lower 145.17 0.22 0.0874 0.2963 3 Fiber 0.04 Basic 0 0.05 0.0388 -- 4 Conserve 1 Equality 17.45 1 0.4693 1.2876 a) Show that the ranges given in the objective function analysis suggest how the solution will change as the price of the corn changes. Solve the problem for the
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IELM_assignment_1_solution - IEEM 202 Assignment#1 Solution...

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