Solve by hand and explain please!

(a) A retail chain has 3 distribution centers to serve 4 regions to meet the demand. The transportation cost between the distribution centers and the regions is given in the following table. Unit Transportation Cost for Regions 2 3 4 A 12 15 13 11 Distribution B 8 16 12 10 Center 9 17 11 13 The demand is expected to be 100, 90, 110, and 120 units in regions 1, 2, 3, and 4 respectively. The distribution centers A, B, and C have shipping capacity of 150, 140, 130 units respectively. i. Construct the transportation table for this problem and initialize this problem using the Northwest corner method. (5 pts) ii. What is the total cost for the initial solution? Is the initial solution optimal? (3 pts) iii. If your answer in part ii is YES, explain WHY? If your answer in part ii is NO, apply one iteration of the transportation simplex method and check whether the resulting solution is optimal or not. (7 pts)