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 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 percentages 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 $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 3,000 barrels of each grade of gasoline. 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 computer. LO.1