Problem:
Optimal Values of the Decision Variable
State all the assumptions and show all the work. Define your decision variables clearly. Briefly explain the constraints and objectives functions and define all unit of measure.
You have been put in charge of the Davidson oil refinery. The refinery produces gas and heating oil from crude oil. Gas sells for $11 per barrel and must have an average grade level of at least 9. Heating oil sells for $6 a barrel and must have an average grade level of at least 7. At most 2,000 barrels of gas and 600 barrels of heating oil can be sold.
Incoming crude can be processed by one of the three methods,. The barrel yield and per barrel cost of each processing method are shown in the following table.
|
|
Grade
|
|
|
Method
|
6
|
8
|
10
|
Cost ($/barrel)
|
|
1
|
0.2
|
0.2
|
0.6
|
3.40
|
|
2
|
0.3
|
0.3
|
0.4
|
3.00
|
|
3
|
0.4
|
0.4
|
0.2
|
2.60
|
For example, if we refine on barrel of incoming crude by method 1, it costs us $3.40 and yields 0.2 barrels of grade 6, 0.2 barrels of grade 8 and 0.6 barrels of grade 10. These costs include the costs of buying the crude oil.
Before being processed into gas and heating oil, grades 6 and 8 may be sent through the catalytic cracker to improve their quality. For $1 per barrel, one barrel of grade 6 can be cracked into a barrel of grade 8. For $1.50 per barrel, a barrel of grade 8 can be cracked into grade 10. The refinery would like to determine how to maximize the refineryâ??s profit.
a) Draw a graphical representation describing this process.
b) Formulate the liner program (LP) model for this situation. (Define all variables)
c) Using your favorite software find the optimal values of the decision variables.