The classical nonlinear programming problem formulation is often too rigid to adequately describe an engineering design problem. Recently a design methodology was developed, based on a problem formulation featuring three types of specifications: hard constraints, soft constraints and objectives. The corresponding mathematical problem is a sequence of constrained 'minimax' optimization problems. Such minimax problems highlight the competition between various specifications and facilitate tradeoff exploration. Accordingly, the new methodology emphasizes designer's intuition and man-machine interaction. In this paper, we demonstrate the crucial role of interaction in an engineering design context. As meaningful interaction is greatly facilitated if suitable sensitivity information is available, we then investigate ways of computing such information , of graphically conveying it to the user.