## 4 Threshold of Rejection  
The defectiveness of the apple, quantified through the area metric, was selected as the key explanatory variable in this study, since it directly correlated with the visual prominence of the defect. Previous research has shown that consumers' attention is often drawn to visible imperfections in food products, making this metric a reliable predictor of consumer reactions [35; 36]. While other variables, such as defect type or texture, could also play a role in consumer decision making, the defect area ratio was chosen due to its straightforward and quantifiable relationship with visual attention and purchase decisions [37]. The analysis of willing-to-pay behavior across the selected apple varieties--Golden Delicious Green, Golden Delicious Yellow, and Idared--provides insights into the interplay between product quality and consumer choices. For the Golden Delicious Green variety, a clear inverse relationship was found between the defective area percentage and the willing-to-pay percentage. As Figure 4 shows, when the defects increased, the likelihood of consumers rebuying decreased significantly, with willing-to-pay rates plummeting from 43% with a 5% defect percentage to just 11% with a 24% defect percentage. The trend of being willing to pay for the Golden Delicious Yellow variety is intricate. Initially, there was a drop in rebuy rates as defects increased, but this decline stabilized around the 40% mark despite defects ranging from 7% to 11%. However, when defects escalated to 14%, a sharper drop to 24% was observed. This pattern suggests a potential threshold of defect tolerance specific to this variety. Conversely, the variety of Idared showcased a more consistent decline in willing-to-pay rates as defects rose. Starting from \begin{table}
\begin{tabular}{l c} \hline \hline
**Level of Defects** & **First Fixation Duration** \\ \hline control & \(0.24\pm 0.11\) \({}^{\mathrm{a}}\) \\ defect level 1 & \(0.45\pm 0.17\) \({}^{\mathrm{c}}\) \\ defect level 2 & \(0.41\pm 0.14\) \({}^{\mathrm{bc}}\) \\ defect level 3 & \(0.45\pm 0.23\) \({}^{\mathrm{c}}\) \\ defect level 4 & \(0.38\pm 0.19\) \({}^{\mathrm{bc}}\) \\ defect level 5 & \(0.42\pm 0.26\) \({}^{\mathrm{c}}\) \\ defect level 6 & \(0.33\pm 0.13\) \({}^{\mathrm{b}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Effect or defect area on first fixation duration. The table presents mean and standard deviation values of the first fixation duration variables, while superscript letters indicate homogenous subgroups created using [PERSON]’s HSD test. a 49% willing-to-pay rate at a 4% defect percentage, the rate dwindled to 15% as defects reached 13%. This steady decline indicates a heightened sensitivity to visible defects in this variety compared to the others. Collectively, these findings highlight the intricate dynamics of consumer perceptions and preferences. While the general trend indicates declining willing-to-pay rates with increasing apple defects, the rate and extent of this decline varied across varieties. Such insights underscore the importance of tailored quality control and marketing strategies for each apple variety. Recognizing these variety-specific nuances and implementing strategies that cater to them can significantly enhance consumer satisfaction and repurchase intent, fostering sustained market success. The formula derived from the polynomial regression is defined as follows:  
\[\text{y}=-42.7953\text{x}^{3}+32.4159\text{x}^{2}-7.5105\text{x}+0.7695 \tag{1}\]  
We used a cubic polynomial formula to fit the relationship between an apple that is defective (x) and the total percentage of repurchases (y). After taking the derivative, we can obtain a 1% increase in defectiveness, which would result in an approximately 1.156% decrease in the repurchase rate. The model's R\({}^{2}\) value was 0.971, suggesting an acceptable fit.