On Martos’ and Charnes-Cooper’s approach vis-a-vis ‘singular points’

In this paper a linear fractional programming problem is studied in presence of ‘singular-points’. It is proved that ‘singular points’, if present, exist at an extreme point of S:¸={x∈Rⁿ∈Ax=b,x∈0∈. It is also shown that a ‘singular point’ is adjacent to an optimal point of S and a characterization of a non-basic vector is obtained, whose entry into the optimal basis in Martos’ approach yields the ‘singular point’.