Tamil Nadu Board of Secondary EducationHSC Commerce Class 12th

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 - Business Mathematics and Statistics

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Sum

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
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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(ai) Chennai 6 8 8 5 30 Madurai 5 11 9 7 40 Trickly 8 9 7 13 50 Demand(bj) 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(ai) Chennai (30)6 8 8 5 30/0 Madurai 5 11 9 7 40 Trickly 8 9 7 13 50 Demand(bj) 35/5 28 32 25 120

Second allocation:

 Bangalore Nasik Bhopal Delhi (ai) Chennai (30)6 8 8 5 30/0 Madurai (5)5 11 9 7 40/35 Trickly 8 9 7 13 50 (bj) 35/5/0 28 32 25 120

Third allocation:

 Bangalore Nasik Bhopal Delhi (ai) Chennai (30)6 8 8 5 30/0 Madurai (5)5 (28)11 9 7 40/35/7 Trickly 8 9 7 13 50 (bj) 35/5/0 28/0 32 25 120

Fourth allocation:

 Bangalore Nasik Bhopal Delhi (ai) 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 (bj) 35/5/0 28/0 32/25 25 120

Fifth allocation:

 Bangalore Nasik Bhopal Delhi (ai) 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 (bj) 35/5/0 28/0 32/25/0 25 120

Final allocation:

 Bangalore Nasik Bhopal Delhi (ai) 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 (bj) 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 x11 = 30

x21 = 5

x22 = 28

x23 = 7

x33 = 25

x34 = 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.

Concept: Transportation Problem
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