Tamil Nadu Board of Secondary EducationHSC Commerce Class 12th

# Determine an initial basic feasible solution to the following transportation problem by using north west corner rule Destination Supply D1 D2 D3 S1 9 8 5 25 Source S2 6 8 4 35 S3 7 6 9 40 - Business Mathematics and Statistics

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Sum

Determine an initial basic feasible solution to the following transportation problem by using north west corner rule

 Destination Supply D1 D2 D3 S1 9 8 5 25 Source S2 6 8 4 35 S3 7 6 9 40 Requirement 30 25 45

#### Solution

Total supply = 25 + 35 + 40 = 100 = sum"a"_"i"

Total requirement = 30 + 25 + 45 = 100 = sum"b"_"j"

Since sum"a"_"i" = sum"b"_"j"

The given transportation problem is balanced and we can find an initial basic feasible solution.

North West Corner Rule

First allocation:

 D1 D2 D3 (ai) S1 (25)9 8 5 25/0 S2 6 8 4 35 S3 7 6 9 40 (bj) 30/5 25 45

Second allocation:

 D1 D2 D3 (ai) S2 (5)6 8 4 35/30 S3 7 6 9 40 (bj) 5/0 25 45

Third allocation:

 D2 D3 (ai) S2 (25)8 4 30/5 S3 6 9 40 (bj) 25/0 45

Fourth allocation:

 D3 (ai) S2 (5)4 5/0 S3 (40)9 40/0 (bj) 45/40/0

We first allow 5 units to cell (S2, D3).

Then balance 40 units we allot to cell (S3, D3).

The final allotment is given as follows

 D1 D2 D3 Supply S1 (25)9 8 5 25 S2 (5)6 (25)8 (5)4 35 S3 7 6 (40)9 40 Requirement 30 25 45

Transportation schedule:

S1 → D1

S2 → D1

S2 → D2

S2 → D3

S3 → D3

i.e x11 = 25

x21 = 5,

x22 = 25

x23 = 5

x33 = 40

Total cost is = (25 × 9) + (5 × 6) + (25 × 8) + (5 × 4) + (40 × 9)

= 225 + 30 + 200 + 20 + 360

= 835

Hence the minimum cost is ₹ 835 by NWC method.

Concept: Transportation Problem
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