*2.4. Box-Behnken Experimental Design*

The Box-Behnken experimental design applied consisted of 12 replicated experiments and 2 replicates in the central point (Table 2). The experiments were randomized to avoid unpredictable effects on the responses. Experimental results were analyzed using the IBM SPSS Statistics 24 software and fitted to polynomials of the form:

$$Y = a\_0 + \sum\_{i=0}^{3} a\_i \mathbf{x}\_i^\* + \sum\_{i=-1}^{2} \sum\_{\substack{j=-2 \\ j \neq i}}^{3} a\_{ij} \mathbf{x}\_i^\* \mathbf{x}\_j^\* + \sum\_{i=-1}^{3} a\_{ii} \mathbf{x}\_i^{\*2} \tag{1}$$

where *Y* is the dependent variable or response, *a*<sup>0</sup> is a scaling constant, *ai* represents the linear coefficients, *aij* the interaction coefficients, *aii* the quadratic coefficients, and *x*<sup>∗</sup> *<sup>i</sup>* the independent variables coded at three levels: −1 (lower limit), 0 (central point), and +1 (upper limit) (Table 2). Analysis of variance (ANOVA) was applied to determine the validity of the quadratic model as well as the statistical significance of the regression coefficients at a 95% confidence level. Moreover, to confirm the model's accuracy, predicted values for each dependent variable were calculated and compared with the experimental ones (Table 2). The equations obtained for each dependent variable were visualized as response surface plots.
