A firm has four manufacturing plants and four warehouses. It is trying to determine the optimal way to ship from its plants to the warehouses. The plant capacities and warehouse requirements are as follows: Plant Capacity Warehouse requirement 1 = 1200 A = 3100 2 = 4200 B = 1800 3 = 5000 C = 2000 4 = 2000 D = 4400 A union requirement prohibits the firm from shipping to warehouse C from Plant 1 (Hint: Use a large cost in this cell when solving with LP so that the program will not assign any units to this cell). The freight charges per unit from each plant to each warehouse are as follows: Plant Warehouse A B C D 1 2 3 4 $9 6 8 7 $5 8 9 9 ---- $11 9 8 $7 6 5 8 Find an initial solution using the North-South rule and find the cost of this solution.