A bicycle manufacturer builds one, three and ten speed models. The bicycles need both aluminum and steel. The company has available 31,170 units of steel and 53,000 units of aluminum. The one, three and ten speed models need, respectively, 6,12 and 15 units of steel and 20,10 and 25 units of aluminum. How many of each type of bicycle should be made in order to maximize profit if the company makes $4 per one speed bike, $8 per three speed bike and $20 per ten speed bike. What is the maximum possible profit?

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