Question 247803: I have a problem in linear programming that I could use assistance with. I am able to use QM for Windows, the issue is that I can't figure out the variables and constraints to enter. Please bear, this is kind of lengthy:
"A refinery blends four petroleum components into three grades of gasoline - regular, premium, and diesal. The maximum quantities available of each component and the cost per barrel are as follows:"
Component 1: Maximum barrels per day = 5000 Cost per Barrel = $9Component 2: Maximum barrels per day = 2400 Cost per Barrel = $7Component 3: Maximum barrels per day = 4000 Cost per Barrel = $12Component 4: Maximum barrels per day = 1500 Cost per Barrel = $6
"To ensure that each gasoline grade retains certain essential characteristics, the refinery has put limits on the percentages of the components in each blend. The limits as well as the selling prices for the various grades are as follows:"
Regular grade: Component specifications - Not less than 40% of component 1, not more than %20 of component 2 and not less than 30% of component 3. The selling price is $12. Premium grade: Component specifications - Not less than 40% of component 3. The selling price is $18 Diesal grade: Component specifications - Not more than 50% of component 2, not less than 10% of component of 1. The selling price is $10.
"The refinery wants to produce at least 3000 barrels of EACH grade of gasoline. Management wishes to determine the optimal mix of the four components that will maximize profit."
Once again, I am able to solve this problem using QM, my only issue is that I cannot determine all the variables and constraints. So far, I have:
Variables: Regular, premium, diesal, component 1, component 2, component 3, component 4. That is only 7 and there is supposed to be 12. I need help identifying the other 5.
Constraints: Maximum barrels per day, and the 6 specifications named earlier. That is only 7 and there should be 13 constraints. I need help identifying the other 6. Once someone can help me to identify all 12 variables and all 13 constraints, I can take it from there. Any help is greatly appreciated. Sorry for the length... Michele
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Write back and I'll give you a quote. This is a complex problem and the preparation of a solution for you will be labor-intensive. I'm not doing this one for free. Maybe someone else will.
John
|
|
|
