1. [20 Pt.) A refinery blends three 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 Cost/Barrel Maximum Barrels Available/Day 6,000 3,000 4,500 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 Selling Price/Barrel R (regular) Component Specifications More than 30% of A Not more than 30% of B Not less than 30% of C Less than 60% of C Not more than 50% of B Exact 10% of A P (premium) D (diesel) 25 15 The refinery wants to produce regular-grade gasoline that is at least 2,000 barrels more than the barrels of premium-grade gasoline. Also, it wants to produce diesel-grade gasoline more than 3,000 barrels. Management wishes to determine the optimal mix of the three components that will maximize profit. 1.1) [5 Pt.] Define the decision variables. 1.2) [5 Pt.] Build the objective function. 1.3) (10 Pt.) Build all the constraints