2. 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 used to produce
the gasolines has a production capacity of 50,000 gallons for the next production period.
Southern Oil's distributors have indicated that demand for the premium gasoline for the next
production period will be at most 20,000 gallons. 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 in order to maximise total profit contribution, and
find the optimal solution.
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