In this paper, we study a class of convex type interval-valued functions on the domain of the product of closed subsets of real numbers. By considering LW order relation on the class of closed intervals, we proposed some optimal solutions. LW convexity concepts and generalized Hukuhara differentiability (viz. delta and nabla) for interval-valued functions yield the necessary and sufficient conditions for interval programming problem. In addition, we compare our results with the results given in the literature. These results may open a new avenue for modeling and solve a different type of optimization problems that involve both discrete and continuous variables at the same time. Definitions, notations and prerequisitesFor a self-contained presentation of our study, we recall briefly the necessary background material.