3 Shale Oil, located on the island of Aruba, has a capacity of 1,500,000 bbl of crude oil per day. The final products from the refinery include three types of unleaded

gasoline with different octane numbers (ON): regular with ON 87, premium with ON 89, and super with ON-92. The refining process encompasses three stages: (1) a distillation tower that producés feedstock (ON 82) at the rate of 2 bbl per bbl of crude oil, (2) a crackér unit that produces gasoline stock (ON-98) by using a portion of the feedstock produced from the distillation tower at the rate of 5 bbl per bbl of feedstock, and (3) a blender unit that blends the gasoline stock from the cracker unit and the feedstock from the distillation tower. The company estimates the net prof- it per barrel of the three types of gasoline to be $6.70, $7.20, and $8.10, respectively. The input capacity of the cracker unit is 200,000 barrels of feedstock a day. The demand limits for regular, premium, and super gasoline are 50,000, 30,000, and 40,000 barrels, respectively, per day. Develop a model for determining the optimum production schedule for the refinery.