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 maximize total profit contribution. If required, round your answers to two decimal places. Let R = number of gallons of regular gasoline produced P = number of gallons of premium gasoline produced
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 maximize total profit contribution. If required, round your answers to two decimal places.
Let R = number of gallons of regular gasoline produced P = number of gallons of premium gasoline produced
Max __________ R + ___________ P s.t. =,>=,<= __________ R + __________ P __________ Grade A crude oil available __________ R + __________ P __________ Production capacity f__________ P __________ Demand for premium R, P __________ - What is the optimal solution?
Gallons of regular gasoline __________ Gallons of premium gasoline __________ Total profit contribution __________ - What are the values and interpretations of the slack variables?
ConstraintValue of Slack Variable
Interpretation1 __________ All available grade A crude oil is used
or
All available grade A crude oil is not used
2 __________ Total production capacity is used
or
Total production capacity is not used
3 __________ Premium gasoline production is 10,000 gallons less than the maximum demand
or
Premium gasoline production is 10,000 gallons greater than the maximum demand
- What are the binding constraints?
Grade A crude oil available Binding or
not biniding
Production capacity Binding or
not biniding
Demand for premium Binding or
not biniding
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