This paper presents a robust linear programming approach for discriminant analysis of two linearly inseparable sets. The proposed method formulates a single linear program that minimizes the average sum of misclassified points from two disjoint sets in n-dimensional space. When the convex hulls of the sets are disjoint, the plane completely separates the sets. When the convex hulls intersect, the method generates a plane that minimizes misclassification errors without imposing extraneous constraints. The effectiveness of the method is demonstrated through successful testing on databases and its application in training a feed-forward neural network with a single hidden layer. The method is formulated as an optimization problem that minimizes the 1-norm of misclassified points. It is shown that this formulation has three key properties: (i) it generates a strictly separating plane when the convex hulls are disjoint, (ii) it minimizes misclassification errors when the convex hulls intersect, and (iii) it does not impose unnecessary constraints. The method is compared with other linear programming approaches, including Smith's linear program, which fails to satisfy these properties in certain cases. The paper also presents computational results using the proposed method on the Wisconsin Breast Cancer Database and the Cleveland Heart Disease Database. The results show that the proposed method outperforms other linear programming approaches in terms of accuracy and efficiency. The method is shown to be robust and effective in handling linearly inseparable sets, making it a preferred choice for such cases. The paper concludes that the proposed linear program is a robust and effective method for discriminant analysis of linearly inseparable sets.This paper presents a robust linear programming approach for discriminant analysis of two linearly inseparable sets. The proposed method formulates a single linear program that minimizes the average sum of misclassified points from two disjoint sets in n-dimensional space. When the convex hulls of the sets are disjoint, the plane completely separates the sets. When the convex hulls intersect, the method generates a plane that minimizes misclassification errors without imposing extraneous constraints. The effectiveness of the method is demonstrated through successful testing on databases and its application in training a feed-forward neural network with a single hidden layer. The method is formulated as an optimization problem that minimizes the 1-norm of misclassified points. It is shown that this formulation has three key properties: (i) it generates a strictly separating plane when the convex hulls are disjoint, (ii) it minimizes misclassification errors when the convex hulls intersect, and (iii) it does not impose unnecessary constraints. The method is compared with other linear programming approaches, including Smith's linear program, which fails to satisfy these properties in certain cases. The paper also presents computational results using the proposed method on the Wisconsin Breast Cancer Database and the Cleveland Heart Disease Database. The results show that the proposed method outperforms other linear programming approaches in terms of accuracy and efficiency. The method is shown to be robust and effective in handling linearly inseparable sets, making it a preferred choice for such cases. The paper concludes that the proposed linear program is a robust and effective method for discriminant analysis of linearly inseparable sets.