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A method is presented for testing the equality of some or all (constrained or unconstrained) optima in a response surface analysis. An estimator of a common location of stationary points is obtained by a standard multivariate testing procedure and a confidence region associated with the common optimum is derived. The procedure is illustrated by the estimation of a common optimum in a multiple response experiment. The multivariate approach facilitates a more efficient estimation of the optimum than the usual univariate response surface analysis and provides additional tests of the response surface model.