# UGCNET-Dec2012-III: 28

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The initial basic feasible solution to the following transportation problem using Vogel’s approximation method is

 $D_1$ $D_2$ $D_3$ $D_4$ Supply $S_1$ 1 2 1 4 30 $S_2$ 3 3 2 1 50 $S_3$ 4 2 5 9 20 Demand 20 40 30 10

$\begin{array}{|c|c|c|c|c|c|} \hline \text{} & \textbf{$D_1$} & \textbf{$D_2$} & \text{$D_3$} & \text{$D_4$} & \textbf{Supply} \\\hline \textbf{$S_1$} & \text{1} & \text{2} & \text{1} & \text{4} & \text{30} \\\hline \textbf{$S_2$} & \text{3} & \text{3} & \text{2} & \text{1} & \text{50} \\\hline \textbf{$S_3$} & \text{4} & \text{2} & \text{5} & \text{9} & \text{20} \\\hline \textbf{Demand} & \text{20} & \text{40} & \text{30} & \text{10} \\\hline \end{array}$

1. $x_{11}=20, x_{13}=10, x_{21}=20, x_{23}=20, x_{24}=10, x_{32}=10$, Total cost = 180
2. $x_{11}=20, x_{12}=20, x_{13}=10, x_{22}=20, x_{23}=10, x_{24}=10$, Total cost = 180
3. $x_{11}=20, x_{13}=10, x_{22}=20, x_{23}=20, x_{24}=10, x_{32}=10$, Total cost = 180
4. None of the above

edited

Ans should be D)none of these as Choice A , B,C  are giving only 90 demand and  supply  allocations whereas given demand and supply are 100.

Method is as per vogel algo summary

1)first calculate penalty(difference between two min values ) for each row and column 2)

now select the column with max penalty and search the least cost in that col/row

4)assign the max allocations and update the row/column demand supply

5)cross out the exhausted row/colum

Repeat the above procedure Correct ans should be X11=20 , X13=10,    X22=20    ,    X23=20   , X24=10, X32=20, Total cost = 180

0
sir, x23  should be 30. isn't it?
0
no , before x23 , x13 will be satisfied due to its lesser cost

Instead if applying entire VAM we cant do a shortcut here. put the option a b and c and check if they are correct or not.

Therefore option D 0
VAM is needed only to find correct soln , here question can be answered  from  options itself

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