## 3 Results and Discussion
### Optimization of \(P_{m\,est}\)
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Terms** & \(F\) & **Coefficient** \\ \hline Constant & & \(-243.705\) \\ \(T_{1}E_{l1}\) & \(92.918\) & \(0.742\) \\ \(E_{l1}^{2}\) & \(961.793\) & \(-9.708\) \\ \(E_{l1}\) & \(326.099\) & \(72.736\) \\ \(T_{2}E_{l2}\) & \(34.06\) & \(0.101\) \\ \(T_{l}V_{u1}\) & \(58.929\) & \(-0.534\) \\ \(V_{u1}\) & \(46.188\) & \(18.324\) \\ \(E_{u1}\) & \(63.689\) & \(21.525\) \\ \(T_{2}E_{u1}\) & \(77.65\) & \(-0.399\) \\ \(T_{2}E_{l1}\) & \(35.845\) & \(0.175\) \\ \(E_{l2}E_{l1}\) & \(16.55\) & \(-0.416\) \\ \(E_{u1}V_{u1}\) & \(19.078\) & \(-1.102\) \\ \(T_{1}E_{u1}\) & \(5.284\) & \(-0.12\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Significance of the terms of Equation (8). (Adapted from Table S3.27 in [27], Supplementary Material (“S3.docx” file)). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(V_{u1}\), & \(E_{l1}\), & \(E_{u1}\), & \(T_{1}\), & \(E_{l2}\), & \(T_{2}\), & \(P_{m\,est}\), \\ \(\mathbf{L}\) & **\% (v/v)** & **\% (v/v)** & \({}^{\circ}\mathbf{C}\) & **\% (v/v)** & \({}^{\circ}\mathbf{C}\) & **g Acetic Acid\(\cdot\)h\({}^{-1}\)** \\ \hline
4.25 & 5.1 & 4.0 & 32 & 4.5 & 28 & 36.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Values of the operational variables needed to maximize \(P_{m\,est}\). Similarly to \((r_{A})_{global\,est}\), the errors in \(P_{m\,est}\) and the operational variables were used to identify the combinations of variables leading to values over the range \(35.9\leq P_{m\,est}\leq 36.6\) g acetic acid\(\cdot\)h\({}^{-1}\) (see Table 9). The ranges of Table 9, at 0.2 unit intervals, allowed a total of 4320 combinations to be identified of which 50 provided a \(P_{m\,est}\) value within the previous range (see Table S3 in file \"S1.docx\" in Supplementary Materials). However, any of the 4320 combinations led to a very high \(P_{m\,est}\) value (32.8-36.6 g acetic acid\(\cdot\)h\({}^{-1}\), which are close to that range). Therefore, any of the combinations of operational variables at values within the ranges of Table 9 would lead to a near-maximum \(P_{m\,est}\) value. Minimizing \(P_{m\,est}\) provided the results of Table 10 (see file \"Optimal_Prod.m\" in Supplementary Materials). The combinations of values of the operational variables leading to minimum \(P_{m\,est}\) values over the range \(14.7\leq P_{m\,est}\leq 15.4\) g acetic acid\(\cdot\)h\({}^{-1}\) were identified similarly to those maximizing this dependent variable. Using the values in the ranges of Table 11 (0.2 unit intervals) provided 360 combinations of which 36 leading to \(P_{m\,est}\) values within the previous range (see Table S4 in file \"S1.docx\" in Supplementary Materials). However, all combinations led to very low \(P_{m\,est}\) values: 14.6-17.1 g acetic acid\(\cdot\)h\({}^{-1}\), which are very close to the minimum value. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(V_{m1}\), & \(E_{11}\), & \(E_{u1}\), & \(T_{1}\), & \(E_{12}\), & \(T_{2}\), & \(P_{m\,est}\), \\ L & \% (\% (\
u/v)) & \({}^{\circ}\)C & \% (\% (\
u/v)) & \({}^{\circ}\)C & g Acetic Acid\(\cdot\)h\({}^{-1}\) \\ \hline
5.75 & 4.0 & 4.0 & 31.9 & 2.5 & 32 & 14.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Values of the operational variables needed to minimize \(P_{m\,est}\). Figure 4: Response surfaces of \(P_{m\,est}\) varying \(E_{11}\) and \(E_{u1}\) (**a**) as well as \(E_{u1}\) and \(E_{i2}\) (**b**), using values from Table 8 for the remaining operational variables. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**End** & \(V_{u1}\)**, L** & \(E_{11}\)**, \% (\% (\
u/v))** & \(E_{u1}\)**, \% (\
u/v)** & \(T_{1}\), \({}^{\circ}\)C** & \(E_{12}\)**, \% (\(\
u/v))** & \(T_{2}\)**, \({}^{\circ}\)C** \\ \hline Lower & 4.25 & 4.9 & 3.7 & 31.3 & 3.5 & 28.0 \\ \(\updownarrow\) & \(\updownarrow\) & \(\updownarrow\) & \(\updownarrow\) & \(\updownarrow\) & \(\updownarrow\) & \(\updownarrow\) \\ Upper & 4.45 & 5.3 & 4.0 & 32.0 & 4.5 & 30.9 \\ \hline \hline \end{tabular}
\end{table}