4. Transportation problem (TP). I 4. J K 3 2 L Supply 8 11 A 5 3 3 2 1 B 14 5 2 6 3 11 Demand 12 7 8 9 Table 1: Detailed data of this minimization TP a. Define variables and find the linear programming formulation of the trans- portation problem (minimize the total cost) as given in transportation table (Table 1)? 2 marks b. Find the initial solution and the corresponding cost by the North-West Corner rule. 3 marks c. Find the initial solution and cost by Vogel Approximation Method. 5 marks d. Write mathematical programming formulation of the assignment problem below; values in matrix give costs of assigning 4 people to 4 jobs; we search for assignments of people to jobs, with the minimum cost. 3 marks Cost peoplex jobs = 24 10 21 11 14 22 10 15 15 17 20 19 11 19 14 13 e. Solve the assignment problem from above with Hungarian method. 7 marks