A company has three plants (P1, P2, P3) and three warehouses (W1, W2, W3). The capacities of plants are 150 units, 150 units, and 250 units, respectively. On the other hand, the demands at the warehouses are 200 units, 100 units, and 300 units. The cost of manufacturing one unit at plant i and shipping it to warehouse j is given in the table below. Cii W1 P1 2 P2 P3 7 8 W2 W3 8 3 2 1 4 5 a) Construct the transportation tableau of the problem. b) Using the Northwest-Corner Rule, determine a starting feasible solution. c) For the initial basic feasible solution, find the entering and leaving variable and write the updated tableau. d) For the updated the tableau in part c, determine the entering variable and leaving variable for this tableau. Write the updated tableau after this iteration. e) Draw the graphical representation of the tableau you find at the end of part d. Calculate the total cost for this tableau.