INTRODUCTIONResponse surface methodology (RSM) is a collectionof statistical and mathematical techniques used in orderto design experiments for adequate response predictions,fit a hypothesized (empirical) model to experimentallyobtained data under the chosen design, as well as tooptimize the conditions for the given process, i.e. toensure the appropriate selection of input variables thatlead to the desired response of a dependent variable [1].There are several different options of the design ofexperiments within RSM, and the options which areused the most are Central Composite Design (CCD)and Box-Behnken Design (BBD). When the analyzedprocess requires adjustments to the experiment whichcannot be carried out using a standard design, some ofcustom designs are used. In that regard, a particularlyinteresting option is the Historical Data design option,which uses data available from the experimentswhich have already been conducted. Specifically,Historical Data creates a blank design layout to acceptcomponent and factor settings and responses from anexisting data set [2].RSM was presented for the first time by Box andWilson in the 1950s, and this methodology is thereforeoften called the Box-Wilson methodology. Detailedinformation on response surface methodology isdescribed in [3]. In general, RSM enables testingeffects and interaction between different process138Papuga S. et al. Foods and Raw Materials, 2022, vol. 10, no. 1, pp. 137–147parameters. It is successfully used to optimize or controlprocesses in various areas of production, research,and engineering [4–8]. Some of the examples refer tooptimization of the medium composition and processparameters for the control of different bioprocesses,including the mead fermentation process [9–13].Mead is an alcoholic beverage obtained byfermentation of honey solution. Honey is a naturalfood produced by honey bees from flower nectar(blossom honey) or plant secretions (honeydew honey).Honey is rich in carbohydrates (mainly glucose andfructose), organic acids, and other components, howeverconcentrations of some components (assimilablenitrogen) can be much lower than those consideredoptimal for fermentation. High sugar contents andlow nitrogen concentration in honey slow downfermentation. It means that the fermentation processrequires optimal pH, temperature, and growthconditions. Therefore, various additives, such as pollen,fruit pulps or juices, citric acid, etc., can be used toimprove alcohol yields, fermentation rates, sensorycharacteristics of mead, etc. [14–18].Fruits and their pulps are rich in carbohydrates,fibers, minerals, vitamin C, carotenoids, as well asphenolic and sulfuric substances. Also, their antioxidantproperties can help maintain balance betweenproduction and elimination of reactive oxygen formsand other related compounds, thereby attenuatingfree radical-induced damage to cells [16–19]. Amongfruits, apples are a widely consumed, rich sourceof phytochemicals (quercetin, catechin, phloridzin,chlorogenic acid, etc.), all of which are strongantioxidants [19]. Apples also contain water, sugars,acids, pectin, tannins, dyed and aromatic substances,mineral substances, starch, cellulose, vitamins, aswell as phenolic compounds and enzymes. All thecomponents give characteristic features to the fruit.Available literature has not mentioned optimizationof honeydew honey as a substrate for obtaining mead.Therefore, this research aimed to assess effects ofthe concentration of added yeast, yeast energizer andthe dry matter content (independent variables) onthe ethanol yield and dry matter content in the finalproduct (dependent variables), with the development ofa corresponding mathematical model. The developedmathematical model can enable better control of theprocess in terms of optimum selection and setting of theprocess parameters.STUDY OBJECTS AND METHODSChemicals and equipment. All chemicals used inthis study were of analytical grade. In our experimentswe used scales (H54AR, Mettler-Toledo, Columbus,USA and PFB 1200-2, KERN & SOHN, Balingen,Germany), a magnetic stirrer (ARE, Velp Scientifica,Usmate, Italy), a vortex (ZX3, Velp Scientifica, Usmate,Italy), a spectrophotometer (Spectronic 1201, MiltonRoy, Ivyland, USA), a pH meter (HI-2211, HannaInstruments, Smithfield, USA), a waterbath (Wisecircu,J.P. Selecta, Abrera, Barcelona, Spain), a refractometer(Leica Abbe Mark II, Reichert Technologies, Depew,USA), and a conductivity meter (HA-2315, HannaInstruments, Smithfield, USA).Physicochemical analyses of honey. The studyobject was honeydew honey from the territory ofthe Republic of Srpska, Bosnia and Herzegovina.The quality characteristics of honeydew honey wasassured by testing it for water content (18.5%), diastaseactivity (47.67), HMF content (5.47 mg/kg), acidity(50.67 mmol/kg), reducing sugars (68.16%), saccharose(2.01%), and electrical conductivity (1.17 ms/cm) asdescribed by Ordinance on methods for control of honeyand other bee products (Official Gazette of BiH no37/2009). The pH was measured with a pH meter (4.33).Honey must preparation. Honeydew honey wasstirred with water in different ratios to obtain requireddry matter content (Tables 1 and 2). The resultantmust was pasteurized at 65°C for 10 min (with regularstirring and skimming off the scum) and then cooledand poured into fermentation flasks. Apple fruit waspressed through a laboratory press to obtain juice thatwas further used in the study to correct the acidity (pHvalues of the must were adjusted to 3.7–4) and as asource of additional nutrition for yeast.The resultant juice was also pasteurized at 65°C for10 min, cooled, and poured into fermentation flasksin amount required for this study (10%). A total of27 samples were prepared (Table 2) for the experiments.Initial dry matter concentrations were measuredrefractometrically. Different amounts of yeast energizerVitaFerm® Ultra F3 (Erbslöh, Geisenheim, Germany)were added into all the samples (Tables 1 and 2). Next,commercial yeast Fermol® Associées (AEB, Italy) wasrehydrated in distilled water at 35–40°C during 30 minand added into the samples in different amounts(Tables 1 and 2).The process of alcoholic fermentation wasconducted at 25°C for 20 days. All fermentations werecarried out in duplicate using a system that consistedof 250 mL flasks containing 180 mL of must andfitted with an airlock to release CO2 produced duringfermentation. Dynamics of the fermentation processwere controlled by weighing the flasks every 24 hthroughout alcoholic fermentation and expressed asthe cumulative mass of produced ethanol per hour.The rate of fermentation depends on concentrationof such inhibitors as ethanol, acetic acid, fatty acids(hexanoic, octanoic, decanoic acid), proteins (enzymes),furfural, hydroxymethylfurfural, etc. The inhibitorsinteract synergistically with high osmotic pressureand the increasing concentration of ethanol duringfermentation [18].General oenological parameters. At the endof fermentations, oenological parameters of mead ‒dry matter content, pH, and ethanol content ‒ weredetermined according to standard methods [20].Design of experiments and mathematicalmodelling. The analysis and processing of previously139Papuga S. et al. Foods and Raw Materials, 2022, vol. 10, no. 1, pp. 137–147obtained experimental data were carried out using theDesign-Expert 11 program (Stat-Ease, Inc. USA) and theHistorical Data Design option. The following variableswere used as independent variables: the initial contentof dry matter (Factor A), yeast (Factor B), and yeastenergizer (Factor C). As dependent (modelled) variableswe used maximum fermentation rate (R3), alcoholcontent (R2), and dry matter content in the product (R1).Table 1 shows the actual and coded values of theabove-mentioned variables, while Table 2 shows thecorresponding design of experiments.The relation between the independent variables (A, B,C) and the modelled variables (R1, R2, R3) is describedby a second-degree polynomial model, by fitting theexperimentally obtained data with the sum of squares.The general form of a second-degree polynomial isgiven using the following equation:Table 1 Coded values of experimental dataFactor Parameter Minimum Maximum Coded low Coded high Mean* SDA Dry matter content, % 16.30 24.40 –1 ↔ 16.30 +1 ↔ 24.40 20.30 (20.20) 3.37B Yeast content, mg/L 150.00 600.00 –1 ↔ 150.00 +1 ↔ 600.00 350.00 (300.00) 190.65C Yeast energizer, mg/L 140.00 500.00 –1 ↔ 140.00 +1 ↔ 500.00 302.33 (267.00) 151.92* The specified mean values represent the arithmetic mean of the lowest and the highest values (the actual, i.e. the used mean valuesof experimental data are given in brackets)Table 2 Historical Data Experimental DesignFactor 1 Factor 2 Factor 3 Response 1 Response 2 Response 3Run A: Dry mattercontent, %B: Yeastcontent, mg/LC: Yeastenergizer, mg/LR1: dry matter afterfermentation, %R2: Alcoholcontent, vol.%R3: Maximumfermentation rate, g/hpH1 16.3 150 140 6.15 8.64 1.16 3.232 16.3 150 267 6.10 8.40 1.20 3.233 16.3 150 500 6.25 8.15 1.34 3.294 16.3 300 140 6.40 8.24 1.27 3.345 16.3 300 267 6.55 7.83 1.24 3.346 16.3 300 500 6.35 8.40 1.28 3.227 16.3 600 140 6.60 8.56 1.03 3.298 16.3 600 267 6.50 8.24 1.11 3.339 16.3 600 500 6.25 7.51 1.45 3.2710 20.2 150 140 6.90 10.62 1.33 3.1811 20.2 150 267 7.85 10.45 2.84 3.3612 20.2 150 500 7.20 10.62 1.47 3.3513 20.2 300 140 7.70 10.20 1.20 3.2114 20.2 300 267 7.60 10.79 2.50 3.3715 20.2 300 500 7.45 10.71 1.44 3.3316 20.2 600 140 7.30 11.13 1.17 3.3117 20.2 600 267 6.70 11.22 2.80 3.4118 20.2 600 500 7.35 10.96 1.93 3.3419 24.4 150 140 11.80 10.88 0.83 3.0720 24.4 150 267 10.45 11.30 1.33 3.1021 24.4 150 500 10.70 11.39 0.88 3.1822 24.4 300 140 10.70 12.24 1.03 3.1123 24.4 300 267 10.00 11.90 1.15 3.1424 24.4 300 500 10.20 11.56 1.15 3.1325 24.4 600 140 10.20 11.73 1.03 3.1426 24.4 600 267 10.45 11.30 1.34 3.1427 24.4 600 500 10.15 11.64 1.73 3.17(1)140Papuga S. et al. Foods and Raw Materials, 2022, vol. 10, no. 1, pp. 137–147where Yi is the response of interest (R1, R2, R3); Xi refersto independent variables (A, B, C); β0 is the constantcoefficient; β1, β2, and β3 are linear coefficients; β12,β13, and β23 are coefficients of interaction between thevariables; β11, β22, and β33 are quadratic coefficients;and e is the model error.The statistical analysis of the developedmathematical models, i.e. the determination of theirstatistical significance, was conducted using the analysisof variance (ANOVA), i.e. the Fisher’s exact test (F-test).The analysis of variance determined the significance ofthe effect of each model parameter on the variance of theoutcome, in comparison with the total variance of all theobserved model parameters.Optimization. In order to determine the initialcontent of dry matter, yeast, and yeast energizerresulting in the maximum alcohol content, with thefermentation rate as consistent as possible, we carriedout the numerical optimization of the developedmathematical models using the Design-Expert 11program (Stat-Ease, Inc.). Prior to the optimization,we selected the objective – the range of numeric valueswithin which we looked for solutions and the level ofsignificance of reaching the set optimization objective,i.e. we selected the corresponding optimizationcriteria (Table 3).RESULTS AND DISCUSSIONWe studied effects of the analyzed independentvariables on the values of dry matter content (R1) andalcohol yield (R2) in the finished product – mead, as wellas on the maximum fermentation rate (R3). Apart fromthe determined design of experiments, Table 2 shows thecorresponding numeric values of the response of interest(R1, R2, and R3) and the measured pH values.The results from Table 2 show that the lowestresidual dry matter content was measured in thesamples which had the lowest dry matter content beforefermentation (samples 1–9), while the samples withthe highest dry matter content before fermentation(samples 19–27) had the highest content of residualdry matter after fermentation. That is related to theduration of the fermentation process (20 days for all thesamples), which means that the dry matter content coulddecrease, and the ethanol content could increase if thefermentation process was extended.According to Pereira et al., residual dry matterconsists of a high number of different compounds:sucrose, maltose, isomaltose, trisaccharides, tetrasaccharides,glycerol, etc [12]. In the research conducted bySavić et al., the dry matter content ranged between 5.2and 11.85% [21]. In our work, the highest ethanol contentwas obtained in samples 19–27, which had the highestdry matter content before fermentation, while the lowestethanol content was in samples 1–9. In the researchconducted by Martínez et al., the ethanol content was10.11 vol. % after day 18 day of fermentation, and it was12.52 vol. % after 26 days [22].The obtained pH values (Table 2) were lower thanthose of the honey solution, most probably due to acidsproduced by yeast during fermentation [23, 24]. ThepH value is a very important parameter for alcoholicfermentation, because yeast cannot ferment under acidicconditions. In this research, the lowest pH value of meadwas 3.07 (sample 19). A low pH value can slow downor even stop the fermentation process, as well as causeincomplete sugar breakdown due to acetic and succinicacid formation, which cause an increase in the contentof undissociated fatty acids [23]. Ammonium ion uptake,which is part of yeast energizer, is associated with theexcretion of proton ions into the medium, therebydecreasing extracellular pH [25].By fitting the data from Table 2 within the regressionanalysis, the corresponding coefficients were determinedin Eq. (1), and the following empirical models weredeveloped:Table 3 Optimization criteriaOptimization objective Range of numeric values Level of significance of the objective (from 1 to 5)Factor A in range 16.3–24.4% not applicableFactor B minimize 150–600 mg/L 3Factor C minimize 140–500 mg/L 4Response R1 none not applicableResponse R2 maximize 7.51–15.00 vol. % 5Response R3 minimize 0.83–2.84 5(2)(3)(4)141Papuga S. et al. Foods and Raw Materials, 2022, vol. 10, no. 1, pp. 137–147The equations given above are written in the form ofthe actual values of the factors (A, B, C), and they maybe used to predict the corresponding response, simplyby inserting the values of A, B, C in the given units. Thegiven equations are normalized and may not be used todetermine the significance of the factors A, B, and C.When analyzing equations where +1 and –1 correspondto the largest and least factor values, respectively, therelative effect of individual factors of the process understudy may be identified by comparing the coefficientsin front of the corresponding factor. Apart from that,equations written in a coded form may be used topredict the response for the given factor level. Theabove-mentioned equations, written in a coded form,are given below:Table 4 ANOVA for quadratic models in terms of coded factor (equations 5, 6, and 7)R1, % R2, vol. % R3, g/hF-value P-value F-value P-value F-value P-valueModel 64.67 < 0.0001 44.43 < 0.0001 3.84 0.0082A-Dry matter content 493.60 < 0.0001 360.36 < 0.0001 0.0592 0.8107B-Yeast 1.31 0.2676 1.10 0.3089 0.8737 0.3630C-Yeast energizer 1.19 0.2900 0.9048 0.3548 3.34 0.0852AB 3.92 0.0640 1.35 0.2615 0.9202 0.3509AC 0.7242 0.4066 0.6884 0.4182 0.0097 0.9226BC 0.1031 0.7521 1.24 0.2817 1.87 0.1888A² 41.78 < 0.0001 37.02 < 0.0001 18.63 0.0005B² 0.0162 0.9003 0.3373 0.5690 0.1417 0.7113C² 0.3903 0.5404 0.0645 0.8025 10.73 0.0045Figure 1 Diagnostics plotsDry matter content Yeast content Yeast energizer(5)(6)(7)The conducted analysis of variance (ANOVA) of thedata (Table 2) proved their statistical significance as awhole, as well as the statistical significance of individualmembers of Eqs. (5)–(7). Table 4 demonstrates theANOVA values for the developed models related tothe effect of the process parameters on the dry mattercontent after fermentation (Eq. (5)), the alcohol content(Eq. (6)) and the maximum fermentation rate (Eq. (7)).The ANOVA was carried out for the equations writtenin a coded form. All the conclusions drawn for theequations written in a coded form apply to the equationsin an actual form as well.142Papuga S. et al. Foods and Raw Materials, 2022, vol. 10, no. 1, pp. 137–147By analyzing the F-values and the P-values forthe quadratic equation (5), i.e. the response R1, it canbe concluded that the developed model is statisticallysignificant as a whole taking into consideration that theF-value of the model is 64.47 and that there is only 0.01%of probability for such a high F-value to occur due tonoise. The P-values below 0.05 indicate that a particularmember of the analyzed equation, to which the givenvalue refers, has a statistically significant effect. In theanalyzed equation, those are the members A and A2. TheP-values above 0.1000 indicate that the given memberof the equation does not have a statistically significanteffect, and in this case, those are B, C, AB, AC,BC, B2, and C2.The quadratic models related to the effect of theprocess parameters on the response R2, i.e. the alcoholcontent (Eq. (6)), have the F-values of 44.43, and thereis only 0.01% of probability for such a high F-value tooccur due to noise. Therefore, it can be concluded thatthe developed model is statistically significant. Likein the previously analyzed equation, the P-valuesof the members A and A2 are below 0.0001, whichmeans that they are statistically significant membersof the given model.The quadratic models related to the effect ofthe process parameters on R3, i.e. the maximumfermentation rate (Eq. (7)), have the F-value of 3.84 andthe P-value of 0.0082, i.e. there is 0.82% of probabilityfor such a high F-value to occur due to noise. Therefore,it can be concluded that the given model is statisticallysignificant. By analyzing the P-values of the individualmembers of Eq. (7), it can be concluded that only themembers A2 and C2 are statistically significant membersof the model, because their P-values are below 0.05 (theP-value of the member A2 is 0.0005, and the P-value ofthe member C2 is 0.0045).The validation of the developed models wasconducted by comparing the experimentally obtaineddata with the corresponding values obtained by using themodel (Fig. 1), and by analyzing the fit statistics fromTable 5. First of all, it is necessary to notice that in allthe experiments there is a satisfactory relation betweenthe measurement signal (response) and noise, which isexpressed by the values of the Adeq Precision parameterabove 4 (Table 5).Figure 1 shows that the actual values in all threecases approximate to the values foreseen by the model,i.e. that the individual values are in the vicinity of theideal line (y = x), and that they are randomly distributedon both sides of the line y = x. This indicates that thereis a correlation between the actual values and the valuesforeseen by the model. This is verified by the high valuesof the determination coefficient (R2), given in Table 5.The table shows that the R2 values for fitted Eqs. (5)and (6) are higher in comparison with the R2 values offitted Eq. (7).However, since all three R2 values are above 0.5, onlyby observing this indicator, it could be concluded that allthree models realistically explain the dependence of theobserved responses (R1, R2, and R3) on the independentvariables (A, B, C). However, that only applies toEqs. (6) and (7). The further analysis of the fit statisticsfrom Table 5 shows that a reasonable agreement betweenthe adjusted R2 and the predicted R2 only exists for thecase of fitted Eqs. (5) and (6), while it is not the case forEq. (7), where there is a significant difference betweenthe two parameters.Specifically, the predicted R2 value (0.2785) isnot close enough to the adjusted R2 value (0.4955),i.e. it is higher than 0.2. This indicates the possibilityof occurrence of a blocking effect as a result of theconduct of experiments in several blocks (a group ofexperimental conditions) or a possible problem withthe model itself and/or individual data. Given the factthat ANOVA showed for this empirical model that onlythe members A2 and C2 are statistically significant, it isassumed that the presence of the other members in themodel contributes to the above-mentioned problem,and the equation is therefore reduced by excludingthe member B, and the members of the interaction AB,AC and BC. The repeated fitting of data from Table 2resulted in the following equation written in the actualand in the coded form respectively:(8)(9)The ANOVA values for the fitted equation (9) inthe coded form show that the equation reduced in sucha manner is also statistically significant as a whole,because the F-value of the model is 8.21, and there isonly 0.03% of probability that such a high value is aresult of noise. Apart from that, the members A2 andC2 are also statistically significant with the P-valuesTable 5 Fit statisticsDry matter content R1 Yeast content R2 Yeast energizer R3 *Yeast energizer R3R² 0.9716 0.9592 0.6701 0.5988Adjusted R² 0.9566 0.9376 0.4955 0.5259Predicted R² 0.9299 0.9005 0.2785 0.3957Adeq Precision 20.6715 17.7830 6.3645 8.3653*Reduced model143Papuga S. et al. Foods and Raw Materials, 2022, vol. 10, no. 1, pp. 137–147of 0.0002 and 0.0027, respectively. The comparisonbetween the experimentally obtained values of themaximum fermentation rate and the values obtained byusing the empirical model described by Eq. (8) or (9)gives the value of the determination coefficient R2 of0.5988, which means that there is a correlation betweenthe values obtained in such a manner. Apart from that,the values of adjusted R2 of 0.5259 and predicted R2of 0.3957, which differ by less than 0.2, indicate thepresence of the given correlation. All this indicatesthat the model reduced in such a manner may be usedfor determining the maximum fermentation rate (R3) inthe given designed space (the tested range of the changeof values of the independent variables). The reductionof the other two models, i.e. fitted Eqs. (2) and (3), andEqs. (5) and (6), was not carried out, because the givenequations have satisfactory values of all the statisticalparameters tested (Fig. 1, Tables 4 and 5).Figure 2 shows the response surface plots whichenable an insight into the behavior of the observeddependent variables (responses R1, R2, and R3) to changethe independent variables and their possible interaction.The plot A (Fig. 2) shows the effect of differentcombinations of the initial content of dry matter andyeast on the dry matter content after fermentation atthe fixed value of yeast energizer of 320 mg/L. The drymatter content after fermentation increased from 6.4 to10.1% with an increase in the initial dry matter contentfrom 16.3 to 24.4% at the value of the yeast content of600 mg/L.An almost identical increase in the dry mattercontent after fermentation from 6.2 to 10.7% with thesame amount of increase in the dry matter content in theinitial raw material was noticed at the value of the yeastcontent of 150 mg/L. Therefore, it can be concludedthat the effect of the yeast content in the initial rawmaterial on the dry matter content after fermentationwas negligible in comparison with the dominant effect ofthe dry matter content in the initial raw material, in thetested range of values of the independent variables.The plot B (Fig. 2) shows the effect of differentcombinations of the dry matter content and yeastenergizer on the dry matter content after fermentation atthe fixed value of the yeast content of 375 mg/L. The drymatter content after fermentation increased from 6.4 to10.3% with an increase in the initial dry matter contentfrom 16.3 to 24.4% at the value of yeast energizer of500 mg/L. A similar increase in the dry matter contentafter fermentation from 6.4 to 10.7% with the sameamount of increase in the dry matter content in theinitial raw material was noticed at the value of yeastenergizer of 140 mg/L. Therefore, it is clear that theeffect of yeast energizer in the initial raw material on thedry matter content after fermentation was negligible incomparison with the dominant effect of the dry mattercontent in the initial raw material, in the tested range ofvalues of the independent variables.Taking into consideration the previous conclusionson the negligible effect of the content of yeast and yeastenergizer in the initial raw material on the dry mattercontent after fermentation, it is expected that differentcombinations of the two given independent variables donot have an effect on the value of the observed response.This is confirmed by the plot F (Fig. 2), which showsthat there is almost no change in the dry matter contentafter fermentation at different combinations of the givenindependent variables and at the fixed dry matter contentin the initial raw material of 20.35%.The plot C (Fig. 2) demonstrates the effect ofdifferent combinations of the content of dry matter andyeast on the alcohol content after fermentation at thefixed value of yeast energizer of 320 mg/L. The alcoholcontent after fermentation increased from 8.14 to 11.73%with an increase in the dry matter content from 16.3 to24.4% at the value of the yeast content of 600 mg/L inthe initial raw material. An almost identical increasein the dry matter content after fermentation from 8.21to 11.31% with the same amount of increase in the drymatter content in the initial raw material was noticed atthe value of the yeast content of 150 mg/L. Therefore,it can be concluded that the effect of the yeast contentin the initial raw material on the alcohol content afterfermentation was negligible in comparison with thedominant effect of the dry matter content in the initialraw material, in the tested range of values of theindependent variables.The plot D (Fig. 2) shows the effect of differentcombinations of the content of dry matter and yeastenergizer on the alcohol content after fermentation at thefixed value of the yeast content of 375 mg/L. The alcoholcontent after fermentation increased from 8.13 to 11.66%with an increase in the dry matter content from 16.3 to24.4% at the value of yeast energizer of 500 mg/L in theinitial raw material. A similar increase in the alcoholcontent after fermentation from 8.47 to 11.66% withthe same amount of increase in the dry matter contentin the initial raw material was noticed at the valueof yeast energizer of 140 mg/L. Therefore, it can beconcluded that the effect of yeast energizer in the initialraw material on the alcohol content after fermentationwas negligible in comparison with the dominant effectof the dry matter content in the initial raw material.Taking into consideration this conclusion, as well as theconclusion drawn from the analysis of the plot C, it canbe concluded that different combinations of the contentof yeast and yeast energizer do not have a significanteffect on the alcohol content after fermentation either,similar to the effect on the dry matter content afterfermentation as shown in the plot F. To ensure visibilityof the work, the corresponding plot is not given in Fig. 2.The plot E (Fig. 2) shows the effect of differentcombinations of the yeast content and the dry mattercontent in the initial raw material on the maximumfermentation rate at the fixed value of yeast energizer of375 mg/L. Unlike the previous plots, the effect of bothobserved independent variables can be clearly noticed144Papuga S. et al. Foods and Raw Materials, 2022, vol. 10, no. 1, pp. 137–147Figure 2 Response surface plots for dry matter content after fermentation (plots A, B, F), Alcohol content (plots C, D) and maximumfermentation rate (plot E). Plots A and C at the fixed content of yeast energizer of 320 mg/L. Plots B, D, and E at the fixed contentof yeast energizer of 375 mg/L. Plot F at the fixed dry matter content in the initial raw material of 20.35%a bc de f145Papuga S. et al. Foods and Raw Materials, 2022, vol. 10, no. 1, pp. 137–147here, which was in accordance with the developedmodel (Eq. (8)), which had two quadratic members. Themaximum fermentation rate increased, went through themaximum, and then decreased, at a particular value ofyeast energizer in the initial raw material.A similar trend of a change in the maximumfermentation rate was noticed with a change in thevalue of yeast energizer in the initial raw material, at aparticular value of the dry matter content in the initialraw material. It is obvious that it is possible to selectparticular combinations of the content of dry matter andyeast energizer in the initial raw material, which wouldgive the maximum alcohol content at the corresponding,i.e. desired values of the fermentation rate and thedry matter content, which was the subject of theoptimization study.Figure 3 shows the results of numerical optimizationof the developed mathematical models. According tothe defined optimization criteria (Table 3), the optimumconditions were the dry matter content of 24.4%, thecontent of yeast of 150 mg/L, and yeast energizer of140 mg/L in the initial raw material. Under suchconditions, the alcohol content obtained afterfermentation was 11.22% with a moderate fermentationrate of 0.86 g/h.The above-mentioned solution had the highestlevel of desirability (0.809) among a total of 65 offeredsolutions. That means that it is possible to select a seriesof combinations of the minimum content of yeast andyeast energizer in the initial raw material which wouldenable the maximum yield of alcohol at a moderatefermentation rate, with the dry matter content within therange of the analyzed numeric values.Figure 3 Optimum conditions and the corresponding responsesCONCLUSIONResponse surface methodology allowed us todevelop empirical mathematical models in the form ofsecond-degree polynomials. The models describe theeffect of the initial content of dry matter, yeast, andyeast energizer on the maximum fermentation rate, thealcohol yield, and the dry matter content in the finishedproduct – mead.The statistical analysis has proved that the initialdry matter content had the statistically significant effecton the content of alcohol and dry mater in the finalproduct. The initial content of yeast and yeast energizerin the tested range of values of the given variable wasnegligible. The developed mathematical models wereused to select optimum fermentation conditions: the drymatter content of 24.4%, the yeast content of 150 mg/L,and the content of yeast energizer of 140 mg/L, in theinitial raw material. Under such conditions, the alcoholyield obtained after 20 days of fermentation was 11.22%at a moderate fermentation rate of 0.86 g/h.CONTRIBUTIONSaša Papuga, Igor Pećanac, Maja Stojković,Aleksandar Savić, and Ana Velemir conceived anddesigned the experiments; performed the experiments;contributed reagents, materials, and analytical tools;and wrote the paper. Saša Papuga analyzed the data,developed mathematical models, and performedparameter optimisation.CONFLICT OF INTERESTThe authors declare no conflict of interest.