Southern gasoline produces two grades of gas: regular and premium. The profit co

Question

Southern gasoline produces two grades of gas: regular and premium. The profit contributions are $.25 per gallon for regular and $.25 per gallon for premium. Each gallon of regular contains .5 gallons of grade A crude oil and each gallon of premium contains .5 gallons of grade A crude oil. For the next production period, southern has 22,000 gallons of grade A crude oil available. The refinery used to produce the gasoline has a production capacity of 45,000 gallons for the next production period. Southern oils distributors have indicated that the demand for the premium gas for the next production period will be at most 21,000 gallons
Formulate a liner programming model and solve it graphically. What are the values of slack and surplus and does this problem have multiple optimal solutions? Southern gasoline produces two grades of gas: regular and premium. The profit contributions are $.25 per gallon for regular and $.25 per gallon for premium. Each gallon of regular contains .5 gallons of grade A crude oil and each gallon of premium contains .5 gallons of grade A crude oil. For the next production period, southern has 22,000 gallons of grade A crude oil available. The refinery used to produce the gasoline has a production capacity of 45,000 gallons for the next production period. Southern oils distributors have indicated that the demand for the premium gas for the next production period will be at most 21,000 gallons
Formulate a liner programming model and solve it graphically. What are the values of slack and surplus and does this problem have multiple optimal solutions?
Formulate a liner programming model and solve it graphically. What are the values of slack and surplus and does this problem have multiple optimal solutions?

Explanation / Answer

Vertex         Lines Through Vertex           Value of Objective
(23000,21000) 0.5x+0.5y = 22000; y = 21000   11000 Maximum
(44000,0)      0.5x+0.5y = 22000; y = 0       11000 Maximum
(0,21000)      y = 21000; x = 0               5250
(0,0)          x = 0; y = 0                   0

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