Question 2[30pts]: Company X manufactures three types of steel at different plants. The time required to manufacture 1 ton of steel (regardless of type) and the costs at each plant are shown in the following table. Each week, 100 tons of each type of steel (1,2, and 3) must be produced. Each plant is open 40 hours per week. (i.) Determine the initial Balanced Transportation Table. (ii.) Determine the initial basic feasible solution using the Vogel's Method. (iii.) Use the initial BFS determined in (ii.) to determine the optimal solution using the Transportation Simplex Method