Before revision:  We show further that the improved upper Fr\'echet--Hoeffding bound is not the dual optimizer of this transport problem .
After revision:  We show that the dual transport problem admits an explicit solution for the function f=1_B, where B is a rectangular subset of \mathbb R^d, and provide an intuitive geometric interpretation of this result. The improved Fr\'echet--Hoeffding bound is not the dual optimizer of this transport problem .