(solution) Set-up the following problem for solution by the Simplex method.

Set-up the following problem for solution by the Simplex method. Express the linear constraints and objective function. Then, add slack variables that convert each constraint into a linear equation. Finally, set-up the initial Simplex tableau. It is not required to solve it.

The Finite Bicycle Manufacturing Company builds racing, touring, and mountain bicycle 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 racing, touring, and mountain models need 17, 27, and 34 units of steel, and 12, 21, and 15 units of aluminum, respectively. How many of each type of bicycle should be made in order to maximize profit if the company makes \$8 per racing bike, \$12 per touring bike, and \$22 per mountain bike? What is the maximum possible profit?

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