function. Desirability is an objective function that ranges from
zero (outside of the limits) to one (at the goal) and its value is
completely dependent on how close the set lower and upper
limits are in relation to the actual optimum.
To establish these criteria, focus was directed toward the
maximization of the applicability and film formation and the
minimization of drying time. According to the data obtained
through the statistical analysis (Table IV; Fig. 1), the objective
of the optimization was to minimize the carbomer concentration
because the inverse proportion of carbomer and PVA
should be maintained in order for high applicability to be
achieved. Moreover, the PVA concentration could not be
lowered because the enhancement of the film-forming performance
is also desired. Both the PVA and the EtOH concentrations
were maximized with careful observation of the
plateau reached at the higher concentrations of both compounds,
thus avoiding a non-efficient increase in these factors
without a proportional increase in the responses.
In this way, under the experimental conditions studied, it
was possible to establish the optimized formulation as that
with 13.0% (w/w) of PVA, 10.0% (w/w) of EtOH, and no
addition of carbomer (Fig. 2; Table V). The combined desirability
function of the formulation was 0.976 and the drying
time, applicability and film-forming performance predicted by