This is a continuation of a recent work(J. Dutta) on a class of non-smooth functions and their subdifferentials. In this note, necessary optimality conditions are derived for the inequality constrained mathematical programming problems involving such non-smooth functions by employing Gordan’s Altative Theorem. This new approach is simpler than the earlier work of Yang and Craven. Mond-Weir type duality theorems are also obtained.