Let A and B be closed, convex bounded subsets of a weakly sequentially complete Banach space E which both are not compact. Then there is linear form x0⁎∈E⁎ does attain its supremum on B. In particular, given any subset A⊂E, if every x⁎∈E⁎ either attains or infimum A, then relatively The same happens for finite family but compact subsets. result only remains true in arbitrary assuming, two σ(E⁎⁎...