A Blend Example A petroleum company produces three grades of motor oil—super, premium, and extra—from three components. The company wants to determine the optimal mix of the three components in each grade of motor oil that will maximize profit. The maximum quantities available of each component and their cost per barrel are as follows: Component Maximum Barrels Available/Day Cost/Barrel 1 4,500 $12 2 2,700 10 3 3,500 14 To ensure the appropriate blend, each grade has certain general specifications. Each grade must have a minimum amount of component 1 plus a combination of other components, as follows: Grade ComponentSpecifications SellingPrice/Barrel Super At least 50% of 1 $23 Not more than 30% of 2 Premium At least 40% of 1 20 Not more than 25% of 3 Extra At least 60% of 1 18 At least 10% of 2 The company wants to produce at least 3,000 barrels of each grade of motor oil. For the blend example in this chapter, if the requirement that “at least 3,000 barrels of each grade of motor oil” was changed to exactly 3,000 barrels of each grade, how would this affect the optimal solution? If the company could acquire more of one of the three components, which should it be? What would be the effect on the total profit of acquiring more of this component?
A Blend Example
A petroleum company produces three grades of motor oil—super, premium, and extra—from
three components. The company wants to determine the optimal mix of the three components
in each grade of motor oil that will maximize profit. The maximum quantities available of each
component and their cost per barrel are as follows:
Component
Maximum Barrels
Available/Day Cost/Barrel
1 4,500 $12
2 2,700 10
3 3,500 14
To ensure the appropriate blend, each grade has certain general specifications. Each grade
must have a minimum amount of component 1 plus a combination of other components, as
follows:
Grade ComponentSpecifications SellingPrice/Barrel
Super At least 50% of 1 $23
Not more than 30% of 2
Premium At least 40% of 1 20
Not more than 25% of 3
Extra At least 60% of 1 18
At least 10% of 2
The company wants to produce at least 3,000 barrels of each grade of motor oil.
For the blend example in this chapter, if the requirement that “at least 3,000 barrels of each grade
of motor oil” was changed to exactly 3,000 barrels of each grade, how would this affect the optimal
solution?
If the company could acquire more of one of the three components, which should it be? What
would be the effect on the total profit of acquiring more of this component?
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