Q.State the rule used to check whether a transportation table's basic feasible solution is non-degenerate. Using the Vogel's Approximation Method solution obtained in Worked Example 3 (3 origins, 3 destinations), verify whether this rule is satisfied.

A basic feasible solution in an $m$-origin, $n$-destination transportation table is non-degenerate only if it uses exactly $m+n-1$ occupied cells — no more, no fewer.

The rule: for a transportation table with $m$ origins and $n$ destinations, a basic feasible solution is non-degenerate if and only if the number of occupied (allocated) cells equals exactly $m+n-1$. If the number of occupied cells is fewer than $m+n-1$, the solution is degenerate and a tiny allocation $\epsilon$ must be placed in an otherwise-empty independent cell before the MODI or Stepping-Stone optimality test can be applied; the number of occupied cells can never exceed $m+n-1$ in a genuine basic feasible solution.

Verification against Worked Example 3: here $m=3$ origins ($O_1,O_2,O_3$) and $n=3$ destinations ($D_1,D_2,D_3$), so $m+n-1=3+3-1=5$. The VAM allocation table found there was:

Counting the occupied cells: $(O_1,D_2), (O_1,D_3), (O_2,D_1), (O_2,D_3), (O_3,D_2)$ — exactly 5 cells.

Confusing the required cell count with $m+n$ (rows plus columns) instead of $m+n-1$; and forgetting that a solution with fewer than $m+n-1$ occupied cells is still usable for optimality testing, but only after adding a tiny $\epsilon$ allocation to an empty cell first.