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Tamil Nadu Board of Secondary EducationHSC Commerce Class 12

Find an initial basic feasible solution of the following problem using northwest corner rule. D1 D2 D3 D4 Supply O1 5 3 6 2 19 O2 4 7 9 1 37 O3 3 4 7 5 34 Demand 16 18 31 25 - Business Mathematics and Statistics

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Question

Find an initial basic feasible solution of the following problem using the northwest corner rule.

  D1 D2 D3 D4 Supply
O1 5 3 6 2 19
O2 4 7 9 1 37
O3 3 4 7 5 34
Demand 16 18 31 25  
Chart
Sum
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Solution

Given the transportation table is

  D1 D2 D3 D4 Supply
(ai)
O1 5 3 6 2 19
O2 4 7 9 1 37
O3 3 4 7 5 34
Demand
(bj)
16 18 31 25 90

Total supply = Total Demand = 90.

The given problem is a balanced transportation problem.

Hence there exists a feasible solution to the given problem.

First allocation:

  D1 D2 D3 D4 (ai)
O1 (16)5 3 6 2 19/3
O2 4 7 9 1 37
O3 3 4 7 5 34
(bj) 16/0 18 31 25 90

Second allocation:

  D1 D2 D3 D4 (ai)
O1 (16)5 (3)3 6 2 19/3/0
O2 4 7 9 1 37
O3 3 4 7 5 34
(bj) 16/0 18/15 31 25 90

Third allocation:

  D1 D2 D3 D4 (ai)
O1 (16)5 (3)3 6 2 19/3/0
O2 4 (15)7 9 1 37/22
O3 3 4 7 5 34
(bj) 16/0 18/15/0 31 25 90

Fourth allocation:

  D1 D2 D3 D4 (ai)
O1 (16)5 (3)3 6 2 19/3/0
O2 4 (15)7 (22)9 1 37/22/0
O3 3 4 7 5 34
(bj) 16/0 18/15/0 31/9 25 90

Fifth allocation:

  D1 D2 D3 D4 (ai)
O1 (16)5 (3)3 6 2 19/3/0
O2 4 (15)7 (22)9 1 37/22/0
O3 3 4 (9)7 5 34/25
(bj) 16/0 18/15/0 31/9/0 25 35

Final allocation:

  D1 D2 D3 D4 (ai)
O1 (16)5 (3)3 6 2 19/3/0
O2 4 (15)7 (22)9 1 37/22/0
O3 3 4 (9)7 (25)5 34/25/0
(bj) 16/0 18/15/0 31/9/0 25/0 35

Transportation schedule: 

O1 → D1

O1 → D2

O2 → D2

O2 → D3

O3 → D3

O3 → D4.

i.e x11 = 16

x12 = 3

x22 = 15

x23 = 22

x33 = 9

x34 = 25.

Total transportation cost = (16 × 5) + (3 × 3) + (15 × 7) + (22 × 9) + (9 × 7) + (25 × 5)

= 80 + 9 + 105 + 198 + 63 + 125

= 580

Thus the minimum cost is ₹ 580 using the northwest comer rule.

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Transportation Problem
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Chapter 10: Operations Research - Exercise 10.1 [Page 250]

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Samacheer Kalvi Business Mathematics and Statistics [English] Class 12 TN Board
Chapter 10 Operations Research
Exercise 10.1 | Q 5 | Page 250

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