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A demonstration of multivariate optical computing is presented using binary dye mixtures consisting of Bismarck Brown and Crystal Violet. Bismarck Brown was treated as the analyte, while Crystal Violet was treated as a random interfering species. First, a multilayer multivariate optical element (MOE) for the determination of Bismarck Brown was designed using a novel nonlinear optimization algorithm. Next, the MOE was fabricated by depositing alternating layers of two metal oxide films (Nb2O5 and SiO2) on a BK-7 glass substrate via reactive magnetron sputtering. Finally, the MOE was tested on 39 binary dye mixtures using a simple T-format prototype instrument constructed for this purpose. For each sample, measurements of the difference between transmittance through the MOE, and the reflectance from the MOE were made. By setting aside some of the samples for instrument calibration and then using the calibration model to predict the remaining samples, a standard error of prediction of 0.69 μM was obtained for Bismarck Brown using a linear regression model.