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
Nonnegativity:
L,C,S >= 0
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View Full DocumentThe 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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 Fall '10
 D
 Operations Research, Optimization, Soybean, Limit superior and limit inferior, 12hour clock

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