Problem: A problem often of concern to managers in the process industry is blending. Consider the task facing the procurement manager of a company that manufactures special additives. She must determine the proper amounts of each raw material to purchase for the production of a certain product. Three raw materials are available. Each gallon of the finished product must have a combustion point of at least 220F. In addition, the gamma content (which causes hydrocarbon pollution) cannot exceed 6% of the volume. The zeta content (which cleans the internal moving parts of engines) must be at least 12% by volume. Each raw material has varying degrees of these characteristics.
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Raw material
Characteristic
|
A
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B
|
C
|
|
Combustion point (F)
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200
|
180
|
280
|
|
Gamma content (%)
|
4
|
3
|
10
|
|
Zeta content (%)
|
20
|
10
|
8
|
Raw material A costs $0.60 per gallon; raw material B, $0.40; and raw material C, $0.50. The procurement manager wishes to minimize the cost of raw materials per gallon of product. What are the optimal proportions of each raw material to use in a gallon of finished product? Hint: Express your decision variables in terms of fractions of a gallon. The sum of the fractions must equal 1.00.
VARIABLE DEFINITIONS
FORMULATION
SOLUTION
You may either state the tools that need to be used to solve the problem, provide the outcomes from use of the tools, or provide a managerial analysis and solution to the problem. Comment on the results found by other students - and provide reasons on why you either agree or disagree.