Hyperspectral imagery, i.e., imagery with more than a hundred spectral bands, is particularly useful for material identification. Since each pixel is a spectral signature, comparing that signature with a library of signatures for known materials allows each pixel's material to be identified as the one with the closest match. The word 'match', of course, must be defined since many measures of matching are used. This material identification process becomes considerably less straightforward, however, when the pixel on the ground includes multiple materials; then the pixel is 'mixed' and no one library signature will match. Rather, a sum of library signatures, with appropriate coefficients of proportionality, that matches the pixel's signature must be determined. The determination of these coefficients of proportionality is termed 'unmixing'. A variety of unmixing methods have been developed and are reported in the literature. This paper addresses a new algorithm based on linear programing (LP), an optimization method borrowed from operations research. Sophisticated LP software is currently available for virtually every computer. The paper is said to be an approach, since the method has not been evaluated to date on real hyperspectral imagery and no claims may yet be made for its performance, although such test and evaluation activities are planned using AVIRIS data from the Jet Propulsion Laboratory.