Sunco processes oil into aviation fuel and heating oil. It costs $40 to purchase each 1000 barrels of oil, which is then distilled and yields 500 barrels of aviation fuel and 500 barrels of heating fuel. Output from the distillation may be sold directly or processed in the catalytic cracker. If sold after distillation without further processing, aviation fuel sells for $60 per 1000 barrels and heating oil sells for $40 per 1000 barrels. It takes 1 hour to process 1000 barrels of aviation fuel in the catalytic cracker, and these 1000 barrels can be sold for $130. It takes 45 minutes to process 1000 barrels of heating oil in the cracker and these 1000 barrels can be sold for $90. Each day, at most 20,000 barrels of oil can be purchased and 8 hours of cracker time are available. Sunco would like to maximize their profits. Provide a linear programming model formulation only; you do not need to identify an optimal solution.
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