An oil company imports crude from three foreign sources and refines it at four refineries. Sources 1, 2, and 3 can ship 8, 10, and 6 units of crude respectively each week. Refineries 1o 4 need 5, 3, 8, and 4 units of crude respectively each week. C;j is the cost ($/unit) of shipping crude from source i to refinery j, and the cost matrix is given below: 1. 4 7 9 10 Cij = 6 4 3 9 6 4 8. (a) Check whether the transportation problem is in balance. If not, obtain a balanced problem and draw its network. (b) Use the Northwest Corner method to find basic feasible solutions, and select the bfs giving the minimum total transportation cost as the initial bfs to apply the Transportation Simplex Method.