What is the linear programming formulation for : A petroleum company produces three grades of motor oil – super, premium, and extra – from three components. The company wants to determine the optimal mix of the three components in each grade of oil that will maximize profit. The maximum quantities available for each component and their cost per barrel are as follows:
Component Maximum Barrels Available/Day Cost/Barrel
1 4,500 $12
2 2,700 $10
3 3,500 $14

To ensure the appropriate blend, each grade has certain general specifications. Each grade must have a minimum amount of component 1 plus a combination of other components, as follows:
Grade Component Specifications Selling Price/Barrel
Super At least 50% of 1
Not more than 30% of 2 $23
Premium At least 40% of 1
Not more than 25% of 3 $20
Extra At least 60% of 1
At least 10% of 2 $18

The company wants to produce at least 3,000 barrels of each grade of motor oil.