Useful relationships between the optimal Kuhn-Tucker multipliers and trade-offs in the multiobjective decision-making problems are developed based on the sensitivity interpretation of such multipliers. Practical and theoretical applications of these results are discussed. The results provide a convenient way for obtaining necessary (trade-off) information for continuing into the analyst-decision-maker interactive phase of the multiobjective decision-making process. This paper further extends the theoretical basis of the Surrogate Worth Trade-off (SWT) Method; a multiobjective optimization method which first appeared in the scientific literature in 1974.