## 7 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Fotation Process Parameters**} & \multicolumn{5}{c}{**Particle Fraction (\(\upmu\)m)**} \\ \cline{2-6}  & **0–20** & **20–40** & **40–71** & **71–100** & **100–125** & **125–200** \\ \hline Number of data & 540 & 540 & 540 & 540 & 540 & 540 \\ Number of GA generations & 30 & 30 & 30 & 30 & 30 \\ Number of NN repetitions & 1000 & 1000 & 1000 & 1000 & 1000 \\ Mean square error & 0.014581 & 0.020541 & 0.021103 & 0.020013 & 0.024458 & 0.030046 \\ Lithological type of copper ore & \multicolumn{5}{c}{sandstone} \\ Flotation time (min) & 22.81 & 30 & 1.316 & 30 & 23.24 & 30 \\ Collector type & \multicolumn{1}{c}{Z} & \multicolumn{1}{c}{Z} & \multicolumn{1}{c}{Z} & \multicolumn{1}{c}{Z} & \multicolumn{1}{c}{Z} \\ Collector dose (g/Mg) & 124.16 & 104.39 & 100 & 166.48 & 168.82 & 169.53 \\ \(\beta\) (\%) & 10.93 & 14.27 & 22.33 & 5.87 & 7.66 & 7.98 \\ \(\vartheta\) (\%) & 0.058 & 0.07 & 0.1 & 0.05 & 0.11 & 0.05 \\ \(\varepsilon\) (\%) & 98.57 & 98.22 & 92 & 96.18 & 95.83 & 90.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: A summary of the optimisation results of the flotation process of particular particle fractions from the Lubin-Glogów copper ore district in the Denver-type flotation machine (E—aqueous solution of ethyl sodium xanthate, Z—aqueous solution of isobutyl sodium xanthate). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Flotation Process Parameters**} & \multicolumn{2}{c}{**Lithological Type of Copper Ore**} \\ \cline{2-4}  & **Dolomite** & **Sandstone** & **Shale** \\ \hline Number of data & 1080 & 1080 & 1080 \\ Number of GA generations & 30 & 30 & 30 \\ Number of NN repetitions & 5000 & 5000 & 1000 \\ Mean square error & 0.035986 & 0.005621 & 0.034646 \\ Optimal particle size (\(\upmu\)m) & 37.23 & 48.06 & 44.02 \\ Flotation time (min) & 1.86 & 1.93 & 21.05 \\ Collector type & E & Z & E \\ Collector dose (g/Mg) & 100 & 100 & 131.52 \\ \(\beta\) (\%) & 10.91 & 24.85 & 5.45 \\ \(\vartheta\) (\%) & 0.23 & 0.26 & 0.32 \\ \(\varepsilon\) (\%) & 89.42 & 95.6 & 97.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: A summary of the optimisation results of the flotation process of particular lithological types from the Lubin-Glogów copper ore district in the Denver-type flotation machine (E—aqueous solution of ethyl sodium xanthate, Z—aqueous solution of isobutyl sodium xanthate, GA—genetic algorithms, NN—neural network). When performing modelling and optimisation in the examined particle fractions, all lithological types were taken into account. The models obtained from NN were burdened with a mean square error of approximately 0.015-0.030. On their basis, optimisation, the results of which are summarised in Table 13, was carried out. Regardless of the particle size distribution of the flotation feed, the best results are obtained during the enrichment of sandstone copper ore. In the following particle fractions: 40-71, 20-40 and 0-20 (\(\upmu\)m), the expected useful component content in the foam product is respectively: 22.33%, 14.27% and 10.93%, while the value of this indicator will reach the level of only 6-8% during enrichment of copper ore with particle size above 71 \(\upmu\)m. Some discrepancies depending on the particle fraction being enriched can be observed based on the analysis of the optimisation results in terms of the expected time of separation of copper-bearing minerals from gangue rock in the first cleaning flotation. The data included in Table 13 indicate a high flotation speed of 40-71 \(\upmu\)m particles. In the majority of the optimisation cases, an aqueous solution of isobutyl sodium xanthate in the following doses was indicated: 100-124 g of collector per 1 Mg of the feed with particle size distribution below 71 \(\upmu\)m and 165-170 g/Mg for the other particle fractions.