A refinery blends three petroleum components into two grades of gasoline – regular and premium. The maximum quantities available of each component and the cost per barrel are as follows: Component Max Barrels Available/Day Cost/Barrel
1 5,000 9
2 2,400 7
3 4,000 12
4 1,500 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
Regular Not less than 40% of 1
Not more than 20% of 2
Not less than 30% of 3 $12
Premium Not less than 40% of 3 $18
Diesel Not more than 50% of 2
Not less than 10% of 1 $10
The refinery wants to produce at least 3000 barrels each of super 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.