A petroleum company produces 3 grades of motor oil – super, premium, and extra – from 3 components. The company wants to determine the optimal mix of the 3 components in each grade of motor oil that will maximize profit. The maximum quantities available of each component and their cost per barrel are as follows:

Component	Maximum Barrels Available per Day	Cost per Barrel
1 2 3	4,500 2,700 3,500	$12 $10 $14

To ensure the appropriate blend, each grade has 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 per Barrel
Super Premium Extra	At least 50% of 1 & Not more than 30% of 2 At least 40% of 1 & Not more than 25% of 3 At least 60% of 1 & At least 10% of 2	$23 $20 $18

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

Formulate a linear programming model for this problem (define your decision variables; write the objective function and all the relevant constraints).

Use the Excel Solver to find the optimal blend mix and the maximum profit. State the optimal blend mix and maximum profit.