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a. 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 ma 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 R+ P s.t. R+ P Grade A crude oil available R+ P Production capacity P ▾ Demand for premium R, P

a. 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 ma 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 R+ P s.t. R+ P Grade A crude oil available R+ P Production capacity P ▾ Demand for premium R, P

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Problem 7-41 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. a. Formulate 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 tota profit contribution. If required, round your answers to two decimal places. L Let R = P = number of gallons of regular gasoline produced number of gallons of premium gasoline produced R+ P s.t. R+ P FRNSRE Grade A crude oil available Production capacity R+ P P 1174 Demand for premium R, P
Transcribed Image Text:Problem 7-41 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. a. Formulate 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 tota profit contribution. If required, round your answers to two decimal places. L Let R = P = number of gallons of regular gasoline produced number of gallons of premium gasoline produced R+ P s.t. R+ P FRNSRE Grade A crude oil available Production capacity R+ P P 1174 Demand for premium R, P
D 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? Value of Slack Variable Constraint 1 2 3 d. What are the binding constraints? Grade A crude oil available Production capacity Demand for premium Non-binding 18000 50000 10000 Interpretation All available grade A crude oil is used Total production capacity is used
Transcribed Image Text:D 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? Value of Slack Variable Constraint 1 2 3 d. What are the binding constraints? Grade A crude oil available Production capacity Demand for premium Non-binding 18000 50000 10000 Interpretation All available grade A crude oil is used Total production capacity is used
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