## 3 Results  
### Model Fitting  
The ultrasound-assisted extraction (UAE) of total phenolics from pumpkin and tomato extracts was optimized using the response surface methodology. This study utilized a central composite design (CCD) to explore the interaction effects between the ethanol concentration, set at 30, 50, or 70% (\(p/v\)) (X\({}_{1}\)), and the time duration, set at 20, 40, or 60 min (X\({}_{2}\)). The experimental matrix was constructed using the central composite design (CCD) and consisted of 13 experimental combinations, incorporating two central points. This configuration facilitated a randomized sequence of experiments to reduce the influence of extraneous variables on the response measurements. The concentrations of total phenolic compounds measured in the dry extracts were as follows: for the tomato extract, the values ranged from 2.95 to 9.91 mg GAE/g; for the pumpkin extract, the range was from 0.98 to 4.35 mg GAE/g. The results are detailed in Table 4.  
The model's overall fit to the data was rigorously evaluated to ascertain the extent to which a combination of the linear, quadratic, and interaction terms could significantly account for the variability observed in the response variables. For tomato extract, the F-value was reported as 92.71 with an associated \(p\)-value nearing zero, while for pumpkin extract, an F-value of 32.61 with a \(p\)-value of 0.000 was noted. These statistical metrics indicate that both models are highly significant. This significance suggests that the factors, namely ethanol concentration and processing time, and their interactions have a substantial collective impact on explaining the variations observed in the response variables (Table 5). \begin{table}
\begin{tabular}{c c} \hline \hline
**Ingredients** & **Quantity in Grams** \\ \hline \hline \
\begin{tabular}{c} Bread flour \\ Sugar \\ Olive oil \\ Fast action yeast \\ Sea salt \\ Water \\ \end{tabular} &
\begin{tabular}{c} 112.0 \\ 2.00 \\ 5.40 \\ 0.60 \\ 1.70 \\ 50.0 \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Preparation of biscuits with pumpkin extract. \begin{table}
\begin{tabular}{c c} \hline \hline
**Ingredients** & **Quantity in Grams** \\ \hline \hline \
\begin{tabular}{c} Oat flakes \\ Sugar \\ Olive oil \\ Fast action yeast \\ Sea salt \\ Water \\ \end{tabular} &
\begin{tabular}{c} 82.0 \\ 0.50 \\ 10.8 \\ 0.60 \\ 1.70 \\ 36.6 \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Preparation of Cereal bars with tomato extract. The individual linear impacts of ethanol and time on the response variables are markedly significant, as evidenced by their substantial F-values (251.73 and 34.14 for ethanol and 25.61 and 67.90 for time, in the cases of tomato and pumpkin, respectively), accompanied by exceedingly low \(p\)-values. These data strongly support the existence of a significant linear relationship between each factor and the corresponding response variable. Furthermore, the quadratic effects of ethanol and time also demonstrate considerable significance, with F-values recorded at 187.21 and 53.62 for tomato, and 10.78 and 48.41 for pumpkin, respectively, alongside similarly low \(p\)-values. These findings suggest that the associations between the factors and the response variables include a quadratic component, indicating the presence of curvature in the relationships that must be considered (Table 5). The interaction between ethanol and time is markedly significant, as evidenced by F-values of 30.98 for tomatoes and 24.56 for pumpkins, coupled with low \(p\)-values. This finding indicates that the impact of one factor (such as ethanol) on the response variable is significantly moderated by the other factor (such as time), and this influence is reciprocal (Table 5).