2. (18 points) Consider the following transportation problem (the numbers given in the table are: the distribution cost from plant i to customer j, supply of each plant and demand of each customer): Customer 1 Customer 2 Customer 3 Supply Plant 1 25 15 5 1000 Plant 2 20 10 500 Plant 3 100 20 3000 Demand 1000 2000 1500 To minimize the distribution cost, solve the problem using Vogel's Methods. Clearly show all steps and explain the steps for full credit. Use the following empty tables to show your solution steps (most probably you will not need that many tables!). 15 30 Plant 1 Customer 1 Customer 2 Customer 3 Remaining Supply Row Penalty (25) (15) (5) (15) (20) (10) (30) (100) (20) Plant 2 Plant 3 Remaining Demand Column Penalty Plant 1 Plant 2 Customer 1 (25) (15) (30) Customer 2 Customer 3 Remaining Supply Row Penalty (15) (5) (20) (100) (10) (20) Plant 3 Remaining Demand Column Penalty Customer 1 Plant 1 Customer 2 Customer 3 Remaining Supply Row Penalty (15) (5) (20) (10) (100) (20) (25) (15) (30) Plant 2 Plant 3 Remaining Demand Column Penalty Customer 2 Plant 1 Customer 1 (25) (15) (30) Customer 3 Remaining Supply Row Penalty (5) (10) (20) (15) (20) (100) Plant 2 Plant 3 Remaining Demand Column Penalty Customer 1 Customer 2 Plant 1 (25) (15) (30) Plant 2 Customer 3 Remaining Supply Row Penalty (5) (10) (20) (15) (20) (100) Plant 3 Remaining Demand Column Penalty Customer 2 Plant 1 Customer 1 (25) (15) (30) (15) (20) (100) Customer 3 Remaining Supply Row Penalty (5) (10) (20) Plant 2 Plant 3 Remaining Demand Column Penalty Plant 1 Plant 2 Plant 3 Remaining Demand Column Penalty Customer 1 (25) (15) (30) Customer 2 (15) (20) (100) Customer 3 Remaining Supply Row Penalty (5) (10) (20) Customer 1 Customer 2 Plant 1 (15) Customer 3 Remaining Supply Row Penalty (5) (10) (20) (25) (15) (30) Plant 2 (20) (100) Plant 3 Remaining Demand Column Penalty Total Cost=