Question 1 [30pts]: A company supplies goods to three customers, who each require 30 units. The company has two warehouses. Warehouse 1 has 40 units available, and warehouse 2 has 30 units available. The costs of shipping 1 unit from warehouse to customer are shown in the following table. There is a penalty for each unmet customer unit of demand: With customer 1 , a penalty cost of $90 is incurred; with customer 2,$80; and with customer 3,$110. (i.) Determine the initial Balanced Transportation Table. (ii.) Determine the initial basic feasible solution using the Northwest Corner Method, Minimum Cost Method and Vogel's Method, and compare their costs. (iii.) Determine the optimal solution using the Transportation Simplex Method