Consider the transportation problem matrix below Dealer 1 2 3 5 Supply Center 1 100 150 200 140 35 400 Center 2 50 70 60 65 80 200 Center 3 40 90 100 150 130 150 Demand 100 200 150 160 140 a. Find the initial solution using the northwest method. Clalculate the corresponding initial cost. b. Find the initial solution using the Lest Cost method. Clalculate the corresponding initial cost. c. Proceed with the necessary iterations to reach the optimal solution starting from the initial solution you got in part b. d. Find an initial solution using Vogel Approximation. Compare it with the optimal solution you gain in part c.