An oil company processes oil into aviation fuel and heating oil. It costs $65,000 to purchase each 1000 barrels of oil, which is then distilled and yields 500 barrels of aviation fuel and 500 barrels of heating oil. Output from the distillation can be sold directly or processed in the catalytic cracker. If sold after distillation without further processing, aviation fuel sells for $80,000 per 1000 barrels, and heating oil sells for $65,000 per 1000 barrels. It takes one hour to process 1000 barrels of aviation fuel in the catalytic cracker, and these 1000 barrels can be sold for $145,000. It takes 45 minutes to process 1000 barrels of heating oil in the cracker, and these 1000 barrels can be sold for $125,000. Each day at most 20,000 barrels of oil can be purchased, and eight hours of cracker time are available. Determine how to maximize the company’s profit.
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