Does the signal contribution function attain its extrema on the boundary of the area of feasible solutions?

The signal contribution function (SCF) was introduced by Gemperline in 1999 and Tauler in 2001 in order to study band boundaries of multivariate curve resolution (MCR) methods. In 2010 Rajko pointed out that the extremal profiles of the SCF reproduce the limiting profiles of the Lawton-Sylvestre plots for the case of noise-free two-component systems. This paper mathematically investigates two-component systems and includes a self-contained proof of the SCF-boundary property for two-component systems. It also answers the question if a comparable behavior of the SCF still holds for chemical systems with three components or even more components with respect to their area of feasible solutions. A negative answer is given by presenting a noise-free three-component system for which one of the profiles maximizing the SCF is represented by a point in the interior of the associated area of feasible solutions.