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

A balanced transportation problem can be formulated as a linear programming model

A balanced transportation problem can be formulated as a linear programming model where Xij is transported from Source i to Destination j is given as follows: Minimize z = 17x11 + 30x12 + 50x13 +8x14 +68x21 +28x22 +40x23 +58x24 +38x31 +8x32 +70x33 + 20X34 subject to X11 + x12 + X13 + X14 = 6 X21 + X22 + x23 + x24 = 10 X31X32 + x33 + x34 = 16 X11 X21 + X31 = 4 X12 + X22 + x32 = 7 = 8 X13 + X23 + X33 X14 + X24X34 Xij 0; = 13 i = 1,2,3 and j = 1,2,3,4. (a) Determine the initial basic feasible solution and initial cost for the given transportation problem by using the northwest corner, least cost and vogel approximation methods through a software (e.g. TORA, MATLAB, or LINGO). You have to indicate the name of the software that you employ. (7 marks) (b) Other than the reason of not able to generate the least cost, discuss why the northwest corner method is considered less sensitive compared to the least cost and vogel approximation methods. (5 marks)

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