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In the following exercise, (a.) use the simplex method to solve the problem and (b.) explain what the values of the slack variables in the optimal solution mean in the context of the problem.

1. A manufacturer of bicycles builds one, three, and ten-speed models. The bicycles are made of both aluminum and steel. The company has available 91,800 units of steel and 42,000 units of aluminum. The one, three, and ten speed models need, respectively, 20, 30, 40 units of steel and 12, 21, and 16 units of aluminum. How many of each type of bicycle should be made in order to maximize profit if the company makes $8.00 per one-speed bike, $12.00 per three-speed, and $24.00 per ten-speed? What is the maximum possible profit?

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