A refinery blends four petroleum components into three grades of gasoline€”regular, premium, and super. The maximum quantities available of each component and the cost per barrel are as follows:

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:

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. Formulate and solve a linear programming model for thisproblem.

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Maximum Barrels Available/day 5000 2400 4000 1500 Cost [barrel) $9.00 7.00 12.00 6.00 Component Component Specifications Not less than 40% of 1 Not more than 20% of 2 Not less 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)] $12.00 Super 18.00 10.00 Premium Regular