An oil company must determine how many barrels of oil to extract during each of the next two years. If the company extracts x1 million barrels during year 1, each barrel can be sold for 80 - x1dollars. If the company extracts x2 million barrels during year 2, each barrel can be sold for 85 - x2dollars. The cost of extracting x1 million barrels during year 1 is 2x12million dollars, and the cost of extracting x2 million barrels during year 2 is 3x22million dollars. A total of 20 million barrels of oil are available, and at most $250 million can be spent on extraction. Determine how the company can maximize its profit (revenues less costs) for the next two years.
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