  A Lagrange multiplier theorem is derived for the case of an imprecise
objective function and a precise constraint. The proof uses methods of analysis
which deal in a direct, algebraic way with imprecisions. They include imprecise
differentiation, and an approximate Fermat Lemma and Implicit Function Theorem.
The tools are the external numbers of Nonstandard Analysis, which are models of
Sorites imprecisions.
