4. A refinery blends four petroleum components into three grades of gasoline regular, premium, and low-lead. The maximum quantities available of each component and the cost per barrel are shown below: Component Maximum Barrels Available/Day Cost/Barrel ( 5000 2400 4000 1500 4 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: Component Specifications Not less than 40% of 1 Not more than 20% of 2 Not more than 30% of 3 Not less than 40% of 3 Not more than 50% of 2 Not less than 10% of 1 Selling Price/Barrel ($) 12 Grade Regular Premiumm Low-Lead 18 The refinery wants to produce at least 3000 barrels of each grade of gasoline. Management wishes to determine the optimal mix of the four components that will maximize profit. Formulate a linear programming model for this problem, and solve using the computer