## 5 Conclusions  
The biosorption onto two new prepared biosorbents based on residual biomass of _Saccharomyces pastorisenius_ micro-encapsulated biosorbent 1) or immobilized (biosorbent 2) in sodium alginate can be applied with good efficiencies in the reactive BRed dye removal from aqueous systems.  
Two empirical models were proposed by an active central compositional rotatable design of \(2^{3}\) order, considering the biosorbent concentration (\(X_{1}\)), dye concentration (\(X_{2}\)) and biosorption time (\(X_{3}\)) as independent variables and the Bred dye removal as decision/response function, or optimization criterion (\(Y_{1}\) and \(Y_{2}\), %). The maximum values of response/decision function (\(Y_{1}\) and \(Y_{2}\)) considered as optimization criterion were de  
Figure 5: Variation of reactive dye removal degree (\(Y_{1}\)) vs. one independent variable (\(X_{i}\)) (two variables kept at the basic value), i.e., (**a**) \(Y_{1}\) = \(Y\)(\(X_{1}\),0,0), (**b**) \(Y_{1}\) = \(Y\)(0,\(X_{2}\),0), or (**c**) \(Y_{1}\) = \(Y\)(0,0,\(X_{3}\)).  
Figure 6: Variation of reactive dye removal degree (\(Y_{2}\)) vs. one independent variable (\(X_{i}\)) (two variables kept at the basic value), i.e., (**a**) \(Y_{2}\) = f(\(X_{1}\),0,0), (**b**) \(Y_{2}\) = f(0,\(X_{2}\),0), or (**c**) \(Y_{2}\) = f(0,0,\(X_{3}\)).  
termined by using the classical optimization methodology and appreciated, in association with the significance and importance of each variable (i.e., Fisher constant (\(F\)), test (\(F_{c}\)), multiple correlation coefficient (\(R_{Y\times 1\times 2\times 3}\)), Student \(t\)-test, experimental and coefficients' dispersion, among others).  
The \(Y_{1}\) decision function (for biosorbent 1) was found to have only a local maximum of 52.878%, working with 70 mg/L BRed dye, 18 g/L of residual yeasts _(Saccharomyces psturianus)_ biomass micro-encapsulated in sodium alginate and after at least 8 h. A distinct maximum for \(Y_{2}\) function (with biosorbent 2) was found to correspond to an immobilized biosorbent concentration of 22.109 g/L (0.553 g per 25 mL), a dye concentration of 48.49 mg/L and biosorption time of 8.799 h for a maximum Bred dye removal of 75.338%.  
The graphical representation of the dye removal variation vs. one or two selected independent variables permits the localization of the optimal variation field of each studied variable. The maximum solutions are encouraging (BRed reactive dye removal > 52% onto biosorbent 1 and >75% onto biosorbent 2), and thus the continuity of this modeling and optimization study is recommended when the utilization of other improved, empirical and programmed (controlled) modeling and optimization methods is possible.  
Conceptualization, C.Z.; methodology, C.Z. and D.S.; software, C.Z.; validation, C.Z.; formal analysis, C.Z.; investigation, C.Z.; resources, D.S.; data curation, C.Z., D.S.; writing--original draft preparation, C.Z.; writing--review and editing, C.Z.; visualization, C.Z. and D.S.; supervision, C.Z.; project administration, D.S.; funding acquisition, D.S. All authors have read and agreed to the published version of the manuscript.  
This research is supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS/CCCDI-UEFISCDI, project number 490 PED/2020, within PNCDI II.  
Not applicable.  
The authors declare no conflict of interest.