The continuity of two functions associated with a maximin problem with connected variables

A function being the sum of two bilinear functions with one and the same first vector argument belonging to a polyhedron and the other two vector arguments belonging to another polyhedron is considered. It is shown that a certain minimum function of this sum and the maximin function of the sum (on the second polyhedron of connected variables) are continuous on corresponding polyhedra, which can be used in solving a maximin problem that is considered in the article.