1. Steps Graph the constraint lines Find the feasible region
Find the slope of the objective line
Find extreme point
Plot objective line through feasible region
Maximize or minimize objective function by shifting line to extreme point
Determine x1 and x2 at this point
Obtain equations for the two lines that intersect
Solve equ 1 for x2
Substitute x2 in equ 2 to obtain value for x1
Substitute x1 in ii above to obtain value for x2

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.

3. Zambonis
CrossChek supplies zambonis to a number of arenas in rural towns across New Brunswick. Some zambonis are sold at a profit, but as part of their “Giving back to the Community” program, CrossChek is required to donate at least 2 more than half of the zambonis it sells at a profit. CrossChek estimates around $10K profit for each zamboni sold, and around a $5K loss for each donated. CrossChek can donate no more than 3. How many should CrossChek sell/donate in order to maximize profit?