## 3 Case Study
The rationale behind such a substantial investment lies in the requirement for high-capacity equipment, a processing plant, and significant infrastructure work, primarily the relocation of the railway that runs through the center of the deposit, while other supporting facilities and equipment have a lesser impact. The spatial relationship of the railway line to the ore body is illustrated in Figure 5.  
For the needs of the stochastic approach, the previously described geological model and the listed parameters provided the foundation for defining probability distributions for each parameter individually. The simulation was conducted for 100 optimizations, requiring the generation of 100 different geological models and 100 values for all parameters. As mentioned earlier, @Risk software (version 8.2.2) and Monte Carlo simulation were utilized to generate probability distributions. It is crucial to recognize that the impact of geological uncertainty was evaluated by simulating the variability of copper, gold, and silver grades, as well as standard density. The distribution established for each parameter remains consistent across every EVB calculation, with the exception of the distribution for grade and standard density. For these two parameters (considering their impact on EBV uncertainty), the distribution is defined around the estimated value for each block individually. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Annual capacity for ore & 10,000,000 t/year \\ \hline Annual capacity for waste & min for 10,000,000 t of ore \\ \hline Slope angles & 37\({}^{\circ}\) \\ \hline Mining recovery & 95\% \\ \hline Processing recovery & 81.5\% for Cu, 46.5\% for Au, 18.6\% for Ag \\ \hline Selling costs & 630.4 USD/t—Cu, 160 USD/kg—Au, 15 USD/kg—Ag \\ \hline Production costs: & 2.5 USD/t—Mining, 5.5 USD/t—Processing \\ \hline Metal price & 7083 USD/t—Cu, 51,831 USD/kg—Au, 648 USD/kg—Ag \\ \hline Discount rate & 10\% \\ \hline Cut-off & 0.15\% \\ \hline Initial investment costs & 400,000,000 USD \\ \hline \end{tabular}
\end{table} 
Table 2: Techno-economic parameters for deterministic pit optimization. The definition of probability distributions and their basic parameters for the stochastic approach was established based on the following:  
* Geological parameters (grade and standard density)--although international standards such as JORC [58] and NI 43-101 [59] do not define the exact limits of permissible error in estimating mineral resources and reserves, various studies [60; 61] suggest that the accuracy of the estimation depends on the degree of exploration and the available data. Following this approach, error intervals of \(\pm\)15% and \(\pm\)30% were adopted in this research, which align with the precision levels characteristic of the Measured and Indicated Resources categories (pert distribution). This ensures transparency in presenting geological uncertainty, which is essential for economic evaluations of mining projects. * Metal prices--the price distributions for copper, gold, and silver were modeled using a beta distribution based on the average prices over the past ten years [56]. However, considering the significant price increase in the last five years and the growing global demand for these metals [62; 63], the chosen distributions suggest a higher probability of future prices exceeding the long-term average values. Specifically, the mean historical prices used as reference points are USD 7083/t for copper, USD 51,831/kg for gold, and USD 648/kg for silver. The distributions reflect an asymmetry toward higher price values, indicating that while there is still some probability of prices falling below these averages, the likelihood of sustained higher prices in the future is significantly greater. This approach provides a more realistic projection for economic evaluations in mining projects, accounting for recent market trends and anticipated demand growth.