While a considerable body of research has investigated the dual response problem, there is a need to reflect decision maker preferences in the simultaneous optimization of the response functions. In this paper, we present a mathematically rigorous approach for incorporating decision maker preferences. By interpreting the Lagrangian as a value function and the Lagrange multiplier as a preference ratio, candidate solutions are explored that reflect decision maker preferences. We consider the dual response approach to the simultaneous maximization of two responses modelled as quadratic forms. A function relating the responses and the value of the Lagrange multiplier is derived, and appropriate restrictions for the multiplier are discussed. We present the approach in algorithmic form and provide an example that demonstrates the application of the method.
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