Using the northwest corner method to find a bfs, find (via the transportation simplex) an optimal solution to the transportation (minimization) problem shown in Table 71.

Solution:
Basic Feasible Solution
I. The cost matrix table is not balanced as the total sum of rows (60 + 50 + 40) is not equal to
the total sum of columns (40 + 70 + 10). Thus we need to add a dummy column to balance
the problem.
12

14

16

0

14

13

19

0

17

15

18

0
II. C11 is the North West element which has a demand of 60 units and supply of 40 units. Assign
the lower of the two in the cell and make suitable deductions.
12
40
14

16

0

14

13

19

0

17

15

18

0
III. Repeat the step II until all the supply and demands are fully utilized.
North West Element : C12
60
50
40
40 70 10 30
0 70 10 30
20
50
40
12
40
14
20
16

0

14

13

19

0

17

15

18

0
IV. North West Element : C22
12
40
14
20
16

0

14

13
50
19

0

17

15

18

0
V. North West Element : C33
12
40
14
20
16

0

14

13
50
19

0

17

15

18
10
0
30
The number of cells allocated is 5. This is less than the number of cells according to the formula
(m+n-1) where m=No. of rows, n-=No. of Columns
m+n-1 = 3=4-1 = 6. Since the allocations are only 5, the solution is degenerate hence we need to
make a dummy allocation of small quantity ‘d’ in the lowest unallocated cell i.e in this case, C21.
Thus the final allocated table is as shown below which gives the basic...