Sunco Oil has three different processes that can be used to manufacture various types of gasoline. Each process involves blending oils in the company’s catalytic cracker. Running process 1 for an hour costs $20 and requires two barrels of crude oil 1 and three barrels of crude oil 2. The output from running process 1 for an hour is two barrels of gas 1 and one barrel of gas 2. Running process 2 for an hour costs $30 and requires one barrel of crude 1 and three barrels of crude 2. The output from running process 2 for an hour is three barrels of gas 2. Running process 3 for an hour costs $14 and requires two barrels of crude 2 and three barrels of gas 2. The output from running process 3 for an hour is two barrels of gas 3. Each month, 4000 barrels of crude 1, at $45 per barrel, and 7000 barrels of crude 2, at $55 per barrel, can be purchased. All gas produced can be sold at the following per-barrel prices: gas 1, $85; gas 2, $90; gas 3, $95. Determine how to maximize Sunco’s profit (revenues less costs). Assume that only 2500 hours of time on the catalytic cracker are available each month.
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