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IE311: Operations Research Assignment 4: Transportation Model, Assignment Problem, Branch-and-Bound Due Date: Tuesday, May 10, 2022, at 11:59 PM via Blackboard. Problem 1 Consider the following transportation problem with the goal of minimizing total cost: Destination 1 Destination 2 Supply Source 1 S3 SI 2000 Source 2 SS $9 2000 Demand 2500 1500 3 The cost (S/ unit) for transporting from source i to demand j is given in the table. The demand for each destination and the supply from each source is also given in the demand row and the supply column, respectively. a) Formulate an LP model for the problem. b) Is this a balanced transportation problem? Why? c) Use the Northwest Comer method to find an initial solution to the problem. What is the total cost? d) Use the Least Cost method to find an initial solution to the problem. What is the total cost? c) Use Vogel's Approximation method to find an initial solution to the problem. What is the total cost in this case? Problem 2 Consider the following transportation problem with the goal of minimizing total cost: Sink 2 Sink 3 Sink 4 Supply Source 1 SS SI S5 S3 Source 2 Source 3 Demand Sink 1 300 S8 S4 500 S9 S3 500 S10 S8 200 SES $4 $2 400 800 500 The cost (5/unit) for transporting from source i to destination is given in the table. The demand for each destination and the supply from each source is also given in the demand row and the supply column, respectively. a) Formulate an LP model for the problem. b) Is this a balanced transportation problem? Why? c) Use the Least Cost method to find an initial solution to the problem. What is the total cost? d) Use the Northwest Comer method to find an initial solution to the problem. What is the total cost? e) Use Vogel's Approximation method to find an initial solution to the problem. What is the total cost in this case? Problem 3 Consider the following assignment problem with the goal of minimizing total cost: Job Person 1 2 3 4 A 12 18 16 15 B 11 16 13 12 C 9 14 10 12 D 12 16 14 13 The cost (in S) for assigning person i (where i - 1, 2, 3, 4) to jobj (where j - A, B, C, D) is given in the table. Use the Hungarian method to find the optimal assignment for the problem. What is the optimal total cost? Problem 4: Solve the following IP using Branch-and-Bound: Min 5x, +6x2 + 7x3 + 8x + 9x Subject to: 3x1 - x2 + x3 + x4 - 2x3 2 2 X: + 3x2 -- X3 - 2x + xs 20 -x1 - x2 + 3x3 + x4 + xs 21 *1.X2, X3, X4,Xs = 0 or 1 Problem 5: Solve the following IP using Branch-and-Bound: Max 3p+49 +2r + s +2+ Subject to: 2p - 4+r+s+tS3 -p+3q+r-s-2ts2 2p+q-r+s +3t 51 P.q. r, s,t in z Problem 6: Consider the following IP problem: Max := 8 x1 + 5.x2 Subject to X1 + X2 56 9.x3 +5.x2