## 3 Results and Discussion  
### Central Composite Design  
The CCD design matrix was applied to all responses, and 30 randomized runs were generated by the software (Table 2) to avoid biases. Across these runs, the TDS ranged between 1.19% and 3.99%. Effects of Brewing Conditions on Total Dissolved Solids (TDS)  
The effects of water temperature, C2 WR, coffee mesh size, and extraction time were assessed using the analysis of variance (ANOVA). A two-factor interaction (2 FI) model was chosen, and the result is shown in Table 3. In this factorial design model, the 2 FI model presented the best fitness of the model as determined by R\({}^{2}\) and the highest \"Adjusted and Predicted R\({}^{2}\)\". Therefore, only two-factor interaction terms were tested, not quadratic terms. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Experimental Run**} & \multicolumn{4}{c}{**Brewing Conditions**} & \multicolumn{2}{c}{**Response**} \\ \cline{2-6}  & **Water** & **Coffee-to-Water Ratio** & **Coffee Mesh Size** & **Extraction Time** & **TDS (\%)** \\  & **Temperature** (\({}^{\circ}\)**C) & **(\(\times 10^{-2}\) g/mL)** & **(mm)** & **(h)** & **TDS (\%)** \\ \hline  
5 & 2.32 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental runs for CCD (TDS). The model equation for calculating the total dissolved solid was achieved using the 2F1 design model. The empirical relationship between the response and the independent variables in the coded units based on the experimental results is given in Equation (7):  
\[ \begin{array}{l}\text{TDS}=2.46122+0.144815\text{A}+1.0562\text{B}+-0.190463 \text{C}+-3.9186\text{e-}17\text{D}+0.0548958\text{AB}+0.0123958\text{AC}+\\ 0.0265625\text{AD}+-0.0548958\text{BC}+0.0159375\text{BD}+0.0159375\text{CD} \end{array}  \tag{7}\]  
The TDS of the CBC ranged between 1.19 and 3.99%. The highest TDS was measured with the following brewing conditions: water temperature of 30 \({}^{\circ}\)C, C2 WR of 1:6, coffee mesh size of 0.25 mm, and extraction time of 24 h. The lowest TDS measurement was observed when the brewing conditions were at the opposite end of the brewing range, i.e., water temperature 4 \({}^{\circ}\)C, C2 WR 1:16, coffee mesh size 0.71 mm, and extraction hour 7 h. ANOVA identified the parameters that significantly influenced the TDS of CBC, with the factors being A: water temperature, B: C2 WR, and C: coffee mesh size, and confirmed that the overall model was highly significant. As for the pairwise interactions, only AB and BC were confirmed to significantly impact TDS. A three-dimensional response surface plot was constructed to determine the optimal levels of each parameter to achieve the TDS of 1.35%, plotting the response (total dissolved solids, %) on the \(z\)-axis against any two independent parameters while maintaining other variables at their optimal values. These surface plots allowed the visualization of the optimum values for each parameter that yielded the desired response. Figure 1a shows the interaction between water temperature and C2 WR. A combination of a higher water temperature (30 \({}^{\circ}\)C) and a higher C2 WR (1:6 g/mL) led to the highest TDS reaching 3.99%, with the coffee mesh size and extraction hours maintaining at 0.48 mm and 15.5 h, respectively. Figure 1b illustrates the interaction between C2 WR and coffee mesh size while keeping the other variables constant. It can be observed that the TDS of CBC increased as the C2 WR increased while the coffee mesh size decreased, with the highest TDS measured at 3.99%, the C2 WR at 1.6 g/mL, and the coffee mesh size at 0.25 mm.