The purpose of this paper is to present the theory and develop an algorithm associated with the exploration of a dual response surface system. The approach is to find conditions on a set of independent or “design” variables which maximize (or minimize) a “primary response” function subject to the condition that a “constraint response” function takes on some specified or desirable value. A method is outlined whereby a user can generate simple two dimensional plots to determine the conditions of constrained maximum primary response regardless of the number of independent variables in the system. He thus is able to reduce to simple plotting the complex task of exploring the dual response system. The procedure that is used to generate the plots depends on the nature of the individual univariate response functions.