Discussion:
Linear Programming: Examining an Oil Company
Linear Programming Question:
A Southern Oil Company produces two grades of gasoline; Regular and Premium. The profit contributions are $0.30 per gallon for regular gasoline and $0.50 per gallon for premium gasoline. Each gallon of regular gasoline contains 0.3 gallons of grade A crude oil and each gallon of premium gasoline contains 0.6 gallons of grade A crude oil. For the next production period, Southern has 18,000 gallons of grade A crude oil available. The refinery that used to produce the gasoline has a production capacity if 50,000 gallons for the next production period. Southern Oils distributors have indicated that demand for the premium gasoline for the next production period will be at most 20,000 gallons.
A) Determine the number of gallons of regular gasoline and the number of gallons of premium gasoline that should be produced in order to maximize total profit contribution. Let R= number of gallons of regular gasoline produced Let P = number of gallons of premium gasoline produced.
B)What is the optimal solution?
- Gallons of regular gasoline
- Gallons of premium gasoline
- Total profit contribution
C) What are the values and interpretations of the slack variables?
D) What are the binding constraints?
- Grade A crude oil available
- Production capacity
- Production capacity