Why does my nonlinear equation system maximize something?

The nonlinear equation system chemical engineering problem in the GAMS formulation was expressed as a nonlinear programming (NLP) optimization model in turn requiring an objective function.  Actually this is somewhat older practice in GAMS as the constrained nonlinear system (CNS) model type was added after this example was initially formulated.  Thus, one could modify the model type to solve constrained nonlinear system yielding the same solution using

However, the CNS model type can only be solved by select solvers and cannot incorporate integer variables.  Formulation as an optimization problem relaxes these restrictions allowing use of for example the MINLP model type plus the other NLP solvers.  Such a formulation involves the choice of a convenient variable to optimize which may not really have any effect since a feasible solution requires all of the simultaneous equations to be solved.  Thus, while ba is maximized, there is no inherent interest in attaining its maximum; it is just convenient.