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
Nonnegativity:
L,C,S >= 0
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 Fall '10
 D
 Optimization, Soybean, Limit superior and limit inferior, Range upper limit, total time requirement

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