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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

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

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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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.

 

  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 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   __________   
  2. What is the optimal solution?

    Gallons of regular gasoline __________ 
    Gallons of premium gasoline __________ 
    Total profit contribution __________ 
  3. 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
  4. 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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