The 3rd interaction of a transportation problem is indicated

The 3rd interaction of a transportation problem is indicated below:

a). Has an optimal solution been found? Give reason to support your answer.

i) Yes ii) NO

Reason:

b). Compute cost of the above solution (Do Not Solve):

1

2

3

Supply

1

4

50

6

0

3

0

50

2

2

50

5

110

8

0

160

3

7

0

3

190

2

60

250

4

4

0

5

0

6

140

140

Demand

100

300

200

600

		1		2		3		Supply
1		4 50		6 0		3 0		50
2		2 50		5 110		8 0		160
3		7 0		3 190		2 60		250
4		4 0		5 0		6 140		140
Demand		100		300		200		600

Solution

1. No, the optimal solution has not been found. since the calculated cost for the allocation at 1-2 and 1-3 are more than the actual cost of these assignments. The number of rows plus number of column -1 is equal to 6 which is the actual number of assignments in our case but since then the optimal solution has not been found.

The cost for 1-2 as calculated by us is 7 whereas the actual cost of this is 6, therefore the cost assigned is higher by 1 and hence optimal allocation has not been made. Similary, the cost for 1-3 is , whereas the original cost for this is , thus our cost is higher by 3. and hence the allocation is incorrect at two place. Thus, we can say that optimal solution has not been found.

2. Cost of the above solution

4*50 + 2*50 + 5*110 + 3*190+2*60 + 6*140 = 2380 answer

	1	2	3	S
1	4	7	6	6
2	2	5	4	4
3	0	3	2	2
4	4	7	6	6
0	-2	1	0
			assumed