The North-West Corner Method allocates purely by position, starting at the top-left cell and moving right or down as each row or column is exhausted, without ever looking at unit cost.

Total supply $=30+50+20=100$ and total demand $=25+35+40=100$, so the problem is already balanced.

Starting at the north-west corner:

1. $(O_1,D_1)$: allocate $\min(30,25)=25$; $D_1$ done, $O_1$ has 5 left.
2. $(O_1,D_2)$: allocate $\min(5,35)=5$; $O_1$ done, $D_2$ has 30 left.
3. $(O_2,D_2)$: allocate $\min(50,30)=30$; $D_2$ done, $O_2$ has 20 left.
4. $(O_2,D_3)$: allocate $\min(20,40)=20$; $O_2$ done, $D_3$ has 20 left.
5. $(O_3,D_3)$: allocate $\min(20,20)=20$; both exhausted together.

Allocation table:

Row totals (30, 50, 20) match the supplies exactly and column totals (25, 35, 40) match the demands exactly, so the allocation is feasible; 5 occupied cells $=m+n-1=3+3-1$, confirming a non-degenerate solution.

Total cost:

Cross-check before costing: verify every row total equals its given supply and every column total equals its given demand — here 30, 50, 20 and 25, 35, 40 both match exactly, and the 5 occupied cells equal $m+n-1$, confirming the allocation is both feasible and non-degenerate before the cost is computed.

Starting the allocation from any cell other than the true north-west (top-left) corner; moving to the next row or column before the current one's supply or demand is fully used up; and allocating a quantity larger than either the remaining row supply or the remaining column demand.