Determine an initial basic feasible solution of the following transportation problem by north west corner method.
Bangalore  Nasik  Bhopal  Delhi  Capacity  
Chennai  6  8  8  5  30 
Madurai  5  11  9  7  40 
Trickly  8  9  7  13  50 
Demand (Units/day) 
35  28  32  25 
Solution
Let B, N, Bh, D represent the destinations Bangalore, Nasik, Bhopal, and Delhi respectively.
Let C, M, T represent the starting places Chennai, Madurai, and Trichy respectively.
The given transportation table is
Bangalore  Nasik  Bhopal  Delhi  Capacity (a_{i}) 

Chennai  6  8  8  5  30 
Madurai  5  11  9  7  40 
Trickly  8  9  7  13  50 
Demand (b_{j}) 
35  28  32  25  120 
Total capacity = Total Demand = 120.
So the given problem is a balanced transportation problem.
Hence there exists a feasible solution to the given problem.
First allocation:
Bangalore  Nasik  Bhopal  Delhi  Capacity (a_{i}) 

Chennai  ^{(30)}6  8  8  5  30/0 
Madurai  5  11  9  7  40 
Trickly  8  9  7  13  50 
Demand (b_{j}) 
35/5  28  32  25  120 
Second allocation:
Bangalore  Nasik  Bhopal  Delhi  (a_{i})  
Chennai  ^{(30)}6  8  8  5  30/0 
Madurai  ^{(5)}5  11  9  7  40/35 
Trickly  8  9  7  13  50 
(b_{j})  35/5/0  28  32  25  120 
Third allocation:
Bangalore  Nasik  Bhopal  Delhi  (a_{i})  
Chennai  ^{(30)}6  8  8  5  30/0 
Madurai  ^{(5)}5  ^{(28)}11  9  7  40/35/7 
Trickly  8  9  7  13  50 
(b_{j})  35/5/0  28/0  32  25  120 
Fourth allocation:
Bangalore  Nasik  Bhopal  Delhi  (a_{i})  
Chennai  ^{(30)}6  8  8  5  30/0 
Madurai  ^{(5)}5  ^{(28)}11  ^{(7)}9  7  40/35/7/0 
Trickly  8  9  7  13  50 
(b_{j})  35/5/0  28/0  32/25  25  120 
Fifth allocation:
Bangalore  Nasik  Bhopal  Delhi  (a_{i})  
Chennai  ^{(30)}6  8  8  5  30/0 
Madurai  ^{(5)}5  ^{(28)}11  ^{(7)}9  7  40/35/7/0 
Trickly  8  9  ^{(25)}7  13  50/25 
(b_{j})  35/5/0  28/0  32/25/0  25  120 
Final allocation:
Bangalore  Nasik  Bhopal  Delhi  (a_{i})  
Chennai  ^{(30)}6  8  8  5  30/0 
Madurai  ^{(5)}5  ^{(28)}11  ^{(7)}9  7  40/35/7/0 
Trickly  8  9  ^{(25)}7  ^{(25)}13  50/25/0 
(b_{j})  35/5/0  28/0  32/25/0  25/0  120 
Transportation schedule: Chennai to Bangalore, Madurai to Bangalore, Madurai to Nasik, Madurai to Bhopal, Trichy to Bhopal, Trichy to Delhi.
i.e x_{11} = 30
x_{21} = 5
x_{22} = 28
x_{23} = 7
x_{33} = 25
x_{34} = 25
The total transportation cost = (30 × 6) + (5 × 5) + (28 × 11) + (7 × 9) + (25 × 7) + (25 × 13)
= 180 + 25 + 308 + 63 + 175 + 325
= 1076
Thus the minimum cost is ₹ 1076 by the northwest comer method.