### x 2

```Southern Oil Company
• 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.
• Each gallon of regular gasoline contains 0.3 gallons of crude A oil and
each gallon of premium gasoline contains 0.6 gallons of crude A oil.
• For the next production period, Southern has 18,000 gallons of crude
A 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 premium
gasoline for the next production period will be at most 20,000 gallons.
• Determine how much of each grade to produce to maximize profit.
Steps
1. Graph the constraint lines
2. Find the feasible region
3. Find the slope of the objective line
4. Find extreme point
i.
Plot objective line through feasible region
ii.
Maximize or minimize objective function by shifting line to
extreme point
5. Determine x1 and x2 at this point
i.
Obtain equations for the two lines that intersect
ii.
Solve equ 1 for x2
iii. Substitute x2 in equ 2 to obtain value for x1
iv. Substitute x1 in ii above to obtain value for x2
```