Discussion
The number of basic variables in an \((m \times n)\) transportation table are :
Answer: A
There are \(m + n - 1\) basic variables.
A transportation problem with \(m\) sources and \(n\) destinations has \(m + n\) supply and demand constraints, but because total supply equals total demand one of them is redundant. So only \(m + n - 1\) constraints are independent, and a basic feasible solution has \(m + n - 1\) basic variables (allocated cells).
\(m + n\) ignores the redundancy, \(m + n + 1\) has no basis, and \(mn\) is the total number of cells, most of which are non-basic. A solution with fewer than \(m + n - 1\) positive allocations is called degenerate.
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