A refinery blends four petroleum components into three grades of gasoline— Regul

Question

A refinery blends four petroleum components into three grades of gasoline— Regular, Premium, and Diesel. The maximum quantities available of each component and the cost per barrel are as follows: Component Maximum Barrels Available/Day Cost/Barrel 1 5000 9 2 2400 7 3 4000 12 4 1500 6 To ensure that each gasoline grade retains certain essential characteristics, the refinery has put limits on the percentage of the components in each blend. The limits as well as the selling prices for the various grades are as follows: Grade Component Specifications Selling Price/Barrel Regualr Not less than 40% of 1 $12 Not more than 20% of 2 Not less than 30% of 3 Premium Not less than 40% of 3 18 Diesel Not more than 50% of 2 10 Not less than 10% of 1 The refinery wants to produce at least 3000 barrels each of Diesel and Premium, and 4000 barrels of Regular. Management wishes to determine the optimal mix of the four components that will maximize profit. a. Formulate a linear programming model for this problem. b. Solve the model by using the Excel Solver.

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Resubmission of Linear programming problem* I posted this a couple days ago and only one person responded but I could not utilize their services. ALl I am asking is if someone can PLEASE help me to simply IDENTIFY the 12 variables and 13 constraints in this problem...DO NOT SOLVE THE PROBLEM!! I have QM for that! I just need help NAMING the variables and constraints! Thanks to any who can help me! I am desperate!*
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.A refinery blends four petroleum components into three grades of gasoline — regular, premium, and low lead. The problem is to determine the optimal usage of the four components that will maximize profit. The availabilities of components and their costs are: availability cost component barrels/day $/barrel #1 5,000 $9.00 #2 2,400 7.00 #3 4,000 12.00 #4 1,500 6.00 Blending formulas and selling price for each grade are: grade specification selling price/barrel regular (R) (1) not less than 40% of #1 $12.00 (2) not more than 20% of #2 (3) not less than 30% of #3 premium (P) (4) not less than 40% of #3 $18.00 low lead (L) (5) not more than 50% of #2 $10.00 (6) not less than 10% of #1 FORMULATION: Decisions: amount of each component used in each grade Variables: xij = barrels of component i used in grade j per day (i = 1, 2, 3, 4 and j = R, P, L) Objective function: max z = 12 (x1R + x2R + x3R + x4R) + 18 (x1P + x2P + x3P + x4P) + 10 (x1L + x2L + x3L + x4L) – 9 (x1R + x1P + x1L) – 7 (x2R + x2P + x2L) – 12 (x3R + x3P + x3L) – 6 (x4R + x4P + x4L) = 3x1R + 5x2R + 6x4R + 9x1P + 11x2P + 6x3P + 12x4P + 1x1L + 3x2L – 2x3L + 4x4L

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