An oil and gas company wants to find the most cost-effective solution to mix three types of crude oil into three different grades of gasoline (87, 89, 91). Each gallon of Type A oil costs $2.10, each gallon of Type B oil costs of $2.30 and each gallon of Type C oil costs $3.00. Grade 87 gas can contain up to 70% of Type A oil, whereas Grade 89 can only contain up to 50% of Type A oil and must at least have 15% of Type C oil. Finally, Grade 91 gas cannot contain more than 10% of Type A oil and must at least have 45% of Type C oil.

For the next production period, the company wants to produce at least 4,000 gallons of Grade 87, 2,000 gallons of Grade 89 and 2,500 gallons of Grade 91 gas. The company has 5,000 gallons of Type A, 6,000 gallons of Type B and 4,000 gallons of Type C oil available.

1. Formulate the complete linear programming model for this situation. What are the decision variables? What is the objective function? What are the constraints?
2. What is the optimal solution? What are the binding constraints?