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uminum and steel. The company has available 38 comma 160 units of steel and 48 comma 380 units of aluminum. The​ 1-, 3-, and​ 10-speed models​ need, respectively, 8​, 12 and 16 units of steel and 15​, 10​, and 20 units of aluminum. The company makes ​$4 per​ 1-speed bike, ​$6 per​ 3-speed, and ​$16 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 x 1​, x 2​, and x 3 represent the numbers of​ 1-, 3-, and​ 10-speed bicycles,​ respectively, and let z be the total profit. ▼ Minimize Maximize zequals nothing subject to 8 x 1 plus 12 x 2 plus 16 x 3 ▼ greater than less than or equals greater than or equals less than nothing 15 x 1 plus 10 x 2 plus 20 x 3 ▼ greater than less than or equals less than greater than or equals nothing x 1greater than or equals​0, x 2greater than or equals​0, x 3greater than or equals0. ​(Do not factor. Do not include the​ $ symbol in your​ answers.) Set up the initial simplex tableau and use the Simplex Method to solve. The maximum profit is ​$ nothing. To get that​ profit, the company should make nothing ​1-speed bicycle(s), nothing ​3-speed bicycle(s), and nothing ​10-speed bicycle(s). ​(Type whole​ numbers.) ​(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. A. When the profit is​ maximized, all of the steel is used but nothing units of aluminum remain unused. ​(Type a whole​ number.) B. When the profit is​ maximized, some of each material remains unused.​ Specifically, nothing units of aluminum and nothing units of steel remain unused. ​(Type whole​ numbers.) C. When the profit is​ maximized, all of the available aluminum and steel is used. D. When the profit is​ maximized, all of the aluminum is used but nothing units of steel remain unused. ​(Type a whole​ number.)