## 3 Results
### Empirical Experimental Modeling
From the experimental planning matrices (Tables 2 and 3), it seems that for the selected experimental variation field of all independent variables exists a _local maximum value_ (\(Y^{\star}=52.878\%\)) for \(Y_{1}\) and a _local maximum_ (\(Y^{\star}=74.184\%\)) for \(Y_{2}\), corresponding to \(X_{1}{}^{\star}=+1.0\), \(X_{2}{}^{\star}=+1.0\) and \(X_{3}{}^{\star}=+1.0\) for both functions (\(Y_{1}\)/\(Y_{2}\)), and to a residual encapsulated yeast biomass concentration of 18 g/L (0.45 g per 25 mL), and, respectively, a residual immobilized yeast-based biomass concentration of 18 g/L (0.45 g per 25 mL), a BRed dye concentration of 70 mg/L, and a S/W contact time for biosorption of 8 h. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Exp. No.** & \(Z_{1}\)**, **(g/L)** & \(Z_{2}\)**, **(mg/L)** & \(Z_{3}\)**, **(h)** & \(X_{1}\)** & \(X_{2}\)** & \(X_{3}\)** & \(Y_{ci}\)** (\%)** & \(Y_{ci}\)** (\%)** & **Deviation (A)** \\ \hline
1 & 6 & 30 & 4 & \(-1\) & \(-1\) & \(-1\) & 13.6243 & 17.9134 & \(-0.3148\) \\
2 & 18 & 30 & 4 & \(1\) & \(-1\) & \(-1\) & 34.7884 & 33.6922 & 0.0315 \\
3 & 6 & 70 & 4 & \(-1\) & \(1\) & \(-1\) & 33.3531 & 38.3054 & \(-0.1485\) \\
4 & 18 & 70 & 4 & \(1\) & \(1\) & \(-1\) & 48.4867 & 54.7038 & \(-0.1282\) \\
5 & 6 & 30 & 8 & \(-1\) & \(-1\) & 1 & 52.6316 & 44.7842 & 0.1491 \\
6 & 18 & 30 & 8 & \(1\) & \(-1\) & 1 & 72.4868 & 65.9042 & 0.0908 \\
7 & 6 & 70 & 8 & \(-1\) & 1 & 1 & 47.0588 & 46.5250 & 0.0113 \\
8 & 18 & 70 & 8 & 1 & 1 & 1 & 74.1839 & 68.2646 & 0.0798 \\
9 & 1.908 & 50 & 6 & \(-1.682\) & 0 & 0 & 36.6774 & 35.3798 & 0.0354 \\
10 & 22.092 & 50 & 6 & 1.682 & 0 & 0 & 63.3226 & 66.9328 & \(-0.0570\) \\
11 & 12 & 16.36 & 6 & 0 & \(-1.682\) & 0 & 34.6505 & 41.5375 & \(-0.1988\) \\
12 & 12 & 83.64 & 6 & 0 & 1.682 & 0 & 51.9091 & 49.6046 & 0.0444 \\
13 & 12 & 50 & 2.64 & 0 & 0 & \(-1.682\) & 44.9438 & 30.7559 & 0.3157 \\
14 & 12 & 50 & 9.36 & 0 & 0 & 1.682 & 69.6629 & 65.8538 & 0.0547 \\
15 & 12 & 50 & 6 & 0 & 0 & 0 & 56.7416 & 60.6002 & \(-0.0680\) \\
16 & 12 & 50 & 6 & 0 & 0 & 0 & 55.3772 & 60.6002 & \(-0.0943\) \\
17 & 0.60 & 50 & 6 & 0 & 0 & 0 & 56.8218 & 60.6002 & \(-0.0665\) \\
18 & 0.60 & 50 & 6 & 0 & 0 & 0 & 58.1059 & 60.6002 & \(-0.0429\) \\
19 & 0.60 & 50 & 6 & 0 & 0 & 0 & 54.8957 & 60.6002 & \(-0.1039\) \\
20 & 0.60 & 50 & 6 & 0 & 0 & 0 & 56.5008 & 60.6002 & \(-0.0726\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental planning matrix in the active central compositional rotatable design of \(2^{3}\) order for static BRed dye biosorption onto biosorbent 2 (residual yeast biomass immobilized in sodium alginate). The analysis of the response functions (\(Y_{1}\) and \(Y_{2}\)) indicate that all \(X_{i}\) independent variables (residual encapsulated or immobilized yeast biomass concentration, dye concentration and biosorption contact time of S/L phases) have an important influence on the reactive Bred dye removal efficiency, a fact which is demonstrated by the values of \(X_{1}\), \(X_{2}\) and \(X_{3}\) coefficients much higher than unity, except in the case of biosorbent 1 (residual yeasts encapsulated biomass) for which the BRed dye concentration (\(X_{2}\)) had an insignificant effect in the experimental \(X_{2}\) variation field (19-170 mgL) toward dye biosorption efficiency. The influence of the \(X_{3}\) variable (S/L phases contact time for biosorption) in \(Y_{1}\) response function is quite similar to that of \(X_{1}\) (biosorbent concentration) (i.e., \(X_{3}\) influence is 1.2244 times higher than that of \(X_{1}\)) for the BRed dye removal (\(Y_{1}\) decision function), and its effects are similar (e.g., the biosorbent concentration (\(X_{1}\)) increasing and the S/L contact time (\(X_{3}\)) increasing in the biosorption process increases the dye removal efficiency, \(Y_{1}\)).