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An oil company must determine how many barrels of oil to extract during each of the next two years. If the company extracts x 1 million barrels during year 1, each barrel can be sold for 80 − x 1 dollars. If the company extracts x 2 million barrels during year 2, each barrel can be sold for 85 − x 2 dollars. The cost of extracting x 1 million barrels during year 1 is 2 x 1 2 million dollars, and the cost of extracting x 2 million barrels during year 2 is 3 x 2 2 million 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.
Practical Management Science
Solutions
Practical Management Science
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 − x1 dollars. If the company extracts x2 million barrels during year 2, each barrel can be sold for 85 − x2 dollars. The cost of extracting x1 million barrels during year 1 is 2x12 million dollars, and the cost of extracting x2 million barrels during year 2 is 3x22 million 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.
To determine: The way the company maximizes its profit for the next 2 years.
Non-linear programming (NLP):
Non-linear programming (NLP) is used in complex optimization problems where the objectives or constraints or sometimes both are non-linear functions of the decision variables. A model can be termed as non-linear for more than one reason.
Explanation of Solution
Model:
Formula:
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