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 producedP=number of gallons of premium gasoline producedMax __________ 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 VariableInterpretation1__________ All available grade A crude oil is used orAll available grade A crude oil is not used 2__________ Total production capacity is usedorTotal production capacity is not used3__________ Premium gasoline production is 10,000 gallons less than the maximum demandorPremium gasoline production is 10,000 gallons greater than the maximum demandWhat are the binding constraints?Grade A crude oil availableBinding ornot binidingProduction capacityBinding ornot binidingDemand for premiumBinding ornot biniding

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Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

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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?

Constraint	Value of Slack Variable	Interpretation
1	__________	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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Gallons of regular gasoline	__________
Gallons of premium gasoline	__________
Total profit contribution	__________