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A bicycle manufacturer builds one, three, and ten speed models. The bicycles need both aluminum and steel. The company has available 47,760 units of steel and 61,425 units of aluminum. The one, three, and ten speed models need respectively 12, 16, and 20 units of steel and 20, 15, and 25 units of aluminum. How many of each bike should be made in order to maximize profit if the company makes $6 per one speed bike, $8 per three speed bike, and $20 per ten speed bike? What is the maximum profit?

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