* A manufacturer of bicycles builds 1-, 3- and 10-speed models. The bicycles are made of both aluminum and steel. The company has available 35,025 units of steel and 46,920 units of aluminum. The 1-, 3-, and 10-speed models need, respectively, 9, 12 and 15 units of steel and 16, 12, and 20 units of aluminum. The company makes $6 per 1-speed bike, $8 per 3-speed, and $20 per 10-speed. Use the simplex method to complete parts (a) and (b). (a) How many of each type of bicycle should be made in order to maximize profit? What is the maximum profit? Set up the linear programming problem. Let x1, x2, and x3 represent the numbers of 1-, 3-, and 10-speed bicycles, respectively, and let z be the total profit. z= subject to 9x₁ + 12x2 + 15x3 16x₁ + 12x2 + 20x3 Xa 20. X20, Ng20. (Do not factor. Do not include the S symbol in your answers.) The maximum profit is $To get that profit, the company should make bicycle(s), and 10-speed bicycle(s). (Type whole numbers.) 1-speed bicycle(s). 3-speed (b) Explain what the values of the slack variables in the optimal solution mean in the context of the problem. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. (b) Explain what the values of the slack variables in the optimal solution mean in the context of the problem. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. OA. When the profit is maximized, all of the available aluminum and steel is used. B. When the profit is maximized, some of each material remains unused. Specifically, units of aluminum units of steel remain unused. and (Type whole numbers.) OC. When the profit is maximized, all of the aluminum is used but (Type a whole number.) OD. When the profit is maximized, all of the steel is used but (Type a whole number.) Click to select your answer(s). units of steel remain unused. units of aluminum remain unused. K