Q4: Linear Programming.

Southern Oil Company produces two grades of gasoline: regular and premium. The profit contributions are $0.55 per gallon for regular gasoline and $0.66 per gallon for premium gasoline. Each gallon of regular gasoline contains 0.45 gallons of grade A crude oil, and each gallon of premium gasoline contains 0.55 gallons of grade A crude oil. For the next production period, Southern has 22,000 gallons of grade A crude oil available. The refinery used to produce the gasoline has a production capacity of 44,000 gallons for the next production period. Southern Oil’s distributors have indicated that demand for premium gasoline for the next production period will be at most 25,000 gallons and they have to produce at least 12,000 gallons of regular gasoline.

  1. Formulate a linear programming model that can be used to determine the number of gallons of regular gasoline and the number of gallons of premium gasoline that should be produced to maximize total profit contribution.
  2. Draw the feasible region.
  3. Find the optimal solution by using the extreme point method.
  4. Are there any slack/surplus? Calculate those if there is any and interpret each one of them.
  5. What are the binding constraints?