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The North West corner method is one of the methods to obtain a basic feasible solution of the transportation problems (special case of LPP).

We will now see how to apply this very simple method to a transportation problem. We will study steps of this method while applying it in the problem itself.

Note that all the explanation is provided in “CYAN” colour. You have to write in examination the only thing which are given in this regular colour under each steps(if any), else you can directly solve matrix of the problem as explained here

**Solution:**

Balance the problem meaning we need to check that if;

$\color{#32c5d4} \Sigma \text { Supply} = \Sigma \text { Demand}$If this holds true, then we will consider the given problem as a balanced problem.

Now, what if it’s not balanced?

If such a condition occurs, then we have to add a dummy source or market; whichever makes the problem balanced. You can watch a video on this type of numerical, which is known as Unbalanced Transportation Problems.

$\to$ The given transportation problem is balanced.

We will start the allocation from the left hand top most corner (north-west) cell in the matrix and make allocation based on availability and demand.

Now, verify the smallest among the availability (Supply) and requirement (Demand), corresponding to this cell. The smallest value will be allocated to this cell and check out the difference in supply and demand, representing that supply and demand are fulfilled, as shown below.

As we have fulfilled the availability or requirement for that row or column respectively, remove that row or column and prepare a new matrix, as shown below.

Repeat the same procedure of allocation of the new North-west corner so generated and check based on the smallest value as shown below, until all allocations are over.

Once all allocations are over, prepare the table with all allocations marked and calculate the transportation cost as follows.

$\begin{aligned} \to \ \text {Transportation cost} &= (40 \times 40) + (3 \times 30) + (4 \times 30) + (2 \times 10) + (8 \times 60) \\ &= \text {Rs } 870 \end{aligned}$

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