Abstract This paper is the first in a number of didactic reports on the application of simplex optimization to analytical methods and instruments. The use of simplex optimization allows rapid determination of the best conditions for analytical purposes. Some basic concepts used in simplex optimization operations are introduced, described, and exemplified. A rapid and highly sensitive method for the colorimetric analysis of formaldehyde via J-acid is derived by means of simplex optimization. The method is over 5 times as sensitive as the original J-acid procedure and almost 10% more sensitive than the simplex optimized chromotropic acid procedure. The average relative standard deviation is about ±1.6%. The limit of detectability is estimated to be 70 ppb.