## 3 Results
### Fermentation Medium Optimization by Central Composite Design  
A central composite design (CCD) based on response surface methods was utilized to enhance the antifungal effects of the _B. velezensis_ BP-1 strain's secondary metabolites. Over 15 trials, the concentrations of semolina flour, peanut root extract, and magnesium oxide were examined. In trial 11, the optimized fermentation broth had the lowest antagonistic activity against _P. arachiicola_ (45.32 % inhibition zone), while in trial 7, it had the maximum activity (90.55 % inhibition zone), as shown in Table 1. For studies employing central composite designs, the response was calculated using multiple regression using second-order polynomial functions. It is stated in the following equation (Equation (3)) that \(Y\) represents the antifungal response (inhibition percentage), and \(a\), \(b\), and \(c\) represent the independent components of semolina flour, peanut root extract, and magnesium sulfate, respectively. \[ \begin{split} Y=-36.4+8.01&\ \mathrm{a}+7.51\ \mathrm{b}+37.7\ \mathrm{c}-0.1272\ \mathrm{a}^{2}-0.2601\mathrm{b}^{2}+6.16\ \mathrm{c}^{2}+0.0333\ \mathrm{a}^{2}\mathrm{b}-4.616\mathrm{a}^{2}\mathrm{c}\\ -1.781\mathrm{b}^{2}\mathrm{c}\end{split}  \tag{3}\]  
ANOVA was used to analyze the data collected from the experiments. The proposed model is significant, as indicated by a Fisher test value of 19.52 and a \(p\)-value of 0.002. In order to demonstrate that a model is adequate, its coefficient of determination (R\({}^{2}\)) must be sufficiently high. As well as determining the trail parameters and their interactions, the R\({}_{2}\) values were also used to estimate the unpredictability. An R\({}^{2}\) value of 0.9723 indicates that the model did not address approximately 2.77 percentage points of variance. Additionally, this model was significant, as shown by an adjusted determination coefficient R\({}^{2}\) of 0.9225 (Table 2). The antagonistic activity of fermented broth was significantly affected by all of the regression coefficients for the linear terms. The antagonistic activity of the fermentation broth was significantly impacted by the addition of semolina flour, peanut root extract, and magnesium sulfate, as shown by their respective \(p\)-values (pa = 0.003, pb = 0.010, and pc = 0.001). Significant increases were seen in the quadratic coefficients, i.e., \(\mathrm{a}^{2}\mathrm{a}\), \(\mathrm{b}^{2}\mathrm{b}\), and \(\mathrm{c}^{2}\mathrm{c}\). The parameter values in these quadrants were found to either boost or reduce the metabolites' activity,  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Source** & **DF** & **Adj SS** & **Adj MS** & **F-Value** & _p-Value_ \\ \hline Model & 9 & 1631.77 & 181.308 & 19.52 & 0.002 \\ Linear & 3 & 815.58 & 271.862 & 29.27 & 0.001 \\ Semolina (a) & 1 & 277.65 & 277.655 & 29.89 & 0.003 \\ Peanut Root Extract (b) & 1 & 147.75 & 147.748 & 15.91 & 0.010 \\ MgSO\({}_{4}\) (c) & 1 & 390.18 & 390.182 & 42.00 & 0.001 \\ Square & 3 & 201.43 & 67.143 & 7.23 & 0.029 \\ \(\mathrm{a}^{2}\mathrm{a}\) & 1 & 37.36 & 37.358 & 4.02 & 0.101 \\ \(\mathrm{b}^{2}\mathrm{b}  
respectively. Table 3 shows that the a\({}^{2}\)b, a\({}^{2}\)c, and b\({}^{2}\)c interaction coefficients of all samples had statistically significant values. The regression models were used to create surface plots to analyze the interactions of the independent variables and the relative importance of the individual ones. The surface plots of the independent variables convey the significance of the variables and the connections between them by processing the action for each paired variable while holding the other variables at their median values. With the optimal concentration of MgSO\({}_{4}\) held constant, the antagonistic activity of semolina flour and peanut root extract is shown in Figure 2A. The graphs show that the antagonistic activity of the secondary metabolites is strongest in the middle range of semolina flour and peanut root extract concentrations, and it drops sharply at the lower and higher concentrations.