• 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: Maximum Barrels Component Available/Day Cost/Barrel 4.000 $10 3.400 8 AWN - 3,200 12 2,200 7 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 30% of 1 $ 14 Not more than 10% of 2 Not less than 40% of 3 Premium Not less than 35% of 3 I 20 Diesel Not more than 40% of 2 12 Not less than 5% of 1. The refinery wants to produce at least 4,000 barrels of each grade of gasoline. Formulate an optimization model that will help the company determine the mix of the four components that will maximize profit. (Note: You do not have to solve the problem - just formulate it!) a. Define the decision variables for this problem. [6 pts] b. Write out the objective function for this problem in terms of the decision variables defined above. [2 pts] c. Write out any constraints necessary for this problem in terms of the decision variables defined above.