Atkinson Ol and Gas Refinery (AOGR) blends four petroleum components into three grades of gasoline - regular, premium, and ultra The maximum quantities available of each component and the cost per barrel are as follows Component Max barrels available per day Cost per barrel (S) 10 8160 5035 7350 4200 2. 14 4. To ensure that each gasoline grade retains specific essential characteristics, the AOGR has limited the percentage of the components in each blend. The limits, as well as the selling prices for the various grades, are as follows Regular. Not less than 18% of component 1, exact 13% ofr Component 3. The seling price of regular- grade gasoline is $12 per barrel Premium Not more than 44% of component 1, Not less than 25% of component 2, not less than 28% of component 3. The selling price of premium-grade gasoline is $14.5 per barrel. Ultra: Not more than 60% of component 3, Not less than 55% of component 2. The selling price of ultra-grade gasoline is $20 per barrel AOGR wants to produce at least 5205 barrets of ultra, at most 7630 barrels premium and exact 4675 barrels of regular. The management wishes to determine the optimal mix of the four components that will maximize profit. (1-a) Clearty define all decision variabie/s. (I-b) Formulate the objective function (1-c) Specity/state all the constraint/s such that only constants appear on the right-hand sides of constraint/s
Atkinson Ol and Gas Refinery (AOGR) blends four petroleum components into three grades of gasoline - regular, premium, and ultra The maximum quantities available of each component and the cost per barrel are as follows Component Max barrels available per day Cost per barrel (S) 10 8160 5035 7350 4200 2. 14 4. To ensure that each gasoline grade retains specific essential characteristics, the AOGR has limited the percentage of the components in each blend. The limits, as well as the selling prices for the various grades, are as follows Regular. Not less than 18% of component 1, exact 13% ofr Component 3. The seling price of regular- grade gasoline is $12 per barrel Premium Not more than 44% of component 1, Not less than 25% of component 2, not less than 28% of component 3. The selling price of premium-grade gasoline is $14.5 per barrel. Ultra: Not more than 60% of component 3, Not less than 55% of component 2. The selling price of ultra-grade gasoline is $20 per barrel AOGR wants to produce at least 5205 barrets of ultra, at most 7630 barrels premium and exact 4675 barrels of regular. The management wishes to determine the optimal mix of the four components that will maximize profit. (1-a) Clearty define all decision variabie/s. (I-b) Formulate the objective function (1-c) Specity/state all the constraint/s such that only constants appear on the right-hand sides of constraint/s
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Atkinson Oil and Gas Refinery (AOGR) blends four petroleum components into three grades of
gasoline - regular, premium, and ultra The maximum quantities available of each component and the
cost per barrel are as follows
Cost per barrel (SY
10
8.
Component
Max barrels available per day
8160
5035
7350
2
14
4.
4200
To ensure that each gasoline grade retains specific essential characteristics, the AOGR has limited
the percentage of the components in each blend. The limits, as well as the selling prices for the
various grades, are as follows:
Regular. Not less than 18% of component 1, exact 13% of Component 3. The selling price of regular-
grade gasoline is $12 per barrel
Premium Not more than 44% of component 1, Not less than 25% of component 2, not less than 28%
of component 3. The selling price of premium-grade gasoline is $14.5 per barrel.
Ultra: Not more than 60% of component 3, Not less than 55% of component 2. The selling price of
ultra-grade gasoline is $20 per barrel.
AOGR wants to produce at least 5205 barrels of ultra, at most 7630 barrels premium and exact 4675
barrels of regular. The management wishes to determine the optimal mix of the four components that
will maximize profit.
(I-a) Clearty define all decision variable/s
(I-b) Formulate the objective function.
(I-c) Specity/state all the constraint/s such that only constants appear on the right-hand
sides of constraint/s
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