Question: Q1. A balanced transportation problem can be formulated as a linear programming model where Xij are the transported from Source i to Destination j is

Q1. A balanced transportation problem can be

Q1. A balanced transportation problem can be formulated as a linear programming model where Xij are the transported from Source i to Destination j is given as follows: Minimize z = 17x11 + 30x22 + 50x12 + 8X14 +68X21 +28X22 + 40x23 +58X24 +38X31 8X32 + 70x3a + 20X34 subject to X11 + X12 + x12 + X14 = 6 X21 + x22 + x 23 + x24 = 10 X1 + X32 + x32 + x34 = 16 411 + x21 = 4 *12+ X22 = 7 *13+ X2a + X32 + =k X24 + X24 +X34 = 13 Xij 20; i = 1,2,3 and j = 1,2,3,4. + X91 + X92 (a) (6) Determine the value of k. (2 marks) Find an initial basic feasible solution and the initial cost for the given transportation problem above by using the northwest corner, least cost and vogel approximation methods through a software (eg. TORA, MATLAB, or LINGO). Justify which method is the best in finding the transportation cost from economic perspective. Indicate the name of the software that you used. (8 marks) Find the optimal solution and optimal transportation cost for the initial basic feasible solution obtained from northwest corner and least cost methods in part (b), by using a software (eg. TORA, MATLAB, or LINGO). Indicate the name of the software that you used. (7 marks) (c) (d) Other than the reason of not able to generate the least cost. Justify why the northwest comer method is considered less sensitive compared to the least cost and vogel approximation methods. (4 marks)

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