Two factories (T1, T 2) manufacture the Super product, which is transported to three cities (K1, K2, K3) for sale. The factories' production volumes are T1:30 and T2:50. The urban demands are K1:20, K2:30 and K3:40. Unit transportation costs between factories and cities are shown in the following table. T1 3 6 T2 7 5 K1 K2 K3 6 4 a) Balance the transportation problem and create a transportation table for it, when the city's K3 demand is to be satisfied in all situations. Shortage costs for other cities can be set to zero. Find the first root solution in the transportation table using the northwest corner method. b) The production volume of factory T1 is increased by ten products. Using the optimality condition of the transportation problem, show that the following transortation table represents an optimal solution. wwwwwwwwwwwwww T1 T2 K1 20 0 20 3 7 K2 20 10 30 6 5 K3 0 40 40 6 4 40 50 90