Tamil Nadu Board of Secondary EducationHSC Commerce Class 12th

# Find the initial basic feasible solution of the following transportation problem: I II III Demand A 1 2 6 7 B 0 4 2 12 C 3 1 5 11 Supply 10 10 10 Using North Wst Corner rule - Business Mathematics and Statistics

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Sum

Find the initial basic feasible solution of the following transportation problem:

 I II III Demand A 1 2 6 7 B 0 4 2 12 C 3 1 5 11 Supply 10 10 10

Using North West Corner rule

#### Solution

Total demand (ai) = 7 + 12 + 11 = 30 and total supply (bj) = 10 + 10 + 10 = 30.

sum"a"_"i" = sum"b"_"j" = Σbj ⇒ the problem is a balanced transportation problem and we can find a basic feasible solution.

North West Comer rule (NWC)

First allocation:

 I II III (ai) A (7)1 2 6 7/0 B 0 4 2 12 C 3 1 5 11 (bj) 10/3 10 10

Second allocation:

 I II III (ai) B (3)0 4 2 12/9 C 3 1 5 11 (bj) 3/0 10 10

Third allocation:

 II III (ai) B (9)4 2 9/0 C 1 5 11 (bj) 10/1 10

Fourth allocation:

 II III (ai) C (1)1 (10)5 11/10/0 (bj) 10/1 10/0

We first allot 1 unit to (C, II) cell and then the balance 10 units to (C, III) cell.

Thus we have the following allocations:

 I II III Demand A (7)1 2 6 7 B (3)0 (9)4 2 12 C 3 (1)1 (10)5 11 Supply 10/3 10 10

Transportation schedule:

A → I

B → I

B → II

C → II

C → III

i.e x11 = 7

x21 = 3

x22 = 9

x32 = 1

x33 = 10

Total cost = (7 × 1) + (3 × 0) + (9 × 4) + (1 × 1) + (10 × 5)

= 7 + 0 + 36 + 1 + 50

= ₹ 94

Concept: Transportation Problem
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