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.
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.
Practical Management Science
6th Edition
ISBN:9781337406659
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![b. What is the optimal solution?
Gallons of regular gasoline
Gallons of premium gasoline
Total profit contribution
Constraint
c. What are the values and interpretations of the slack variables? If an amount is zero, enter "0".
1
2
3
Value of Slack
Variable
40,000 X
10,000 X
d. What are the binding constraints?
40,000
10,000 ✓
All available grade A crude is used ✓
Total production capacity is used ✔
0 X Premium gasoline production is 10,000 gallons greater than the maximum demand X
Grade A crude oil available
Production capacity
Demand for premium
$ 17,000
Interpretation
Binding ✓
Binding ✓
Binding X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbf7838de-33b1-4c9b-b444-de4b7c84d20a%2F9220d378-be65-4541-8d06-aaac48ff06bc%2Fe2kzqlj_processed.png&w=3840&q=75)
Transcribed Image Text:b. What is the optimal solution?
Gallons of regular gasoline
Gallons of premium gasoline
Total profit contribution
Constraint
c. What are the values and interpretations of the slack variables? If an amount is zero, enter "0".
1
2
3
Value of Slack
Variable
40,000 X
10,000 X
d. What are the binding constraints?
40,000
10,000 ✓
All available grade A crude is used ✓
Total production capacity is used ✔
0 X Premium gasoline production is 10,000 gallons greater than the maximum demand X
Grade A crude oil available
Production capacity
Demand for premium
$ 17,000
Interpretation
Binding ✓
Binding ✓
Binding X
![Problem 2-41
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 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. If your answer is zero, enter "0". If the
constant is "1" it must be entered in the box.
Let R =
P =
Max ✓
s.t.
number of gallons of regular gasoline produced
number of gallons of premium gasoline produced
0.3 ✓ R+
0.3 ✓ R+
1 ✓ R+
0.5 ✓ P
0.6 ✓ PSV
1 ✓ PSV
1
✓ PSV
R, PZ V
18,000 ✓ Grade A crude oil available
50,000 ✓
20,000 ✓
0
✓
Production capacity
Demand for premium](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbf7838de-33b1-4c9b-b444-de4b7c84d20a%2F9220d378-be65-4541-8d06-aaac48ff06bc%2F58s7uz_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 2-41
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 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. If your answer is zero, enter "0". If the
constant is "1" it must be entered in the box.
Let R =
P =
Max ✓
s.t.
number of gallons of regular gasoline produced
number of gallons of premium gasoline produced
0.3 ✓ R+
0.3 ✓ R+
1 ✓ R+
0.5 ✓ P
0.6 ✓ PSV
1 ✓ PSV
1
✓ PSV
R, PZ V
18,000 ✓ Grade A crude oil available
50,000 ✓
20,000 ✓
0
✓
Production capacity
Demand for premium
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