A petroleum company produces 3 grades of motor oil â super, premium, and extra â from 3 components. The company wants to determine the optimal mix of the 3 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 per Day Cost per Barrel
1 4,500 $12
2 2,700 $10
3 3,500 $14
To ensure the appropriate blend, each grade has general specifications. Each grade must have a minimum amount of component 1 plus a combination of other components, as follows:
Grade Component Specifications Selling Price per Barrel
Super At least 50% of 1 & Not more than 30% of 2 $23
Premium At least 40% of 1 & Not more than 25% of 3 $20
Extra At least 60% of 1 & At least 10% of 2 $18
The company wants to produce at least 3,000 barrels of each grade of motor oil.
Formulate a linear programming model for this problem (define your decision variables; write the objective function and all the relevant constraints). For this question, follow the answer given under blending problems discussed on pages 166-171 in the textbook.
Use the Excel Solver to find the optimal blend mix and the maximum profit. State the optimal blend mix and maximum profit.