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The irradiation of ¹⁷⁶Yb with deuterons offers a promising pathway for the production of the theranostic radionuclide ¹⁷⁷Lu. To optimize this process, calculations integrating deuteron transport, isotope production, and decay have been performed. In pure ¹⁷⁶Yb, the undesired production of ^174g+mLu occurs at higher deuteron energies, corresponding to a distribution slightly shallower than that of ¹⁷⁷Lu. Hence, ^174g+mLu can be effectively filtered out by employing either a low-energy deuteron beam or stacked foils. The utilization of stacked foils enables the production of ¹⁷⁷Lu using a high-energy linear accelerator. Another unwanted isotope, ^176mLu, is produced roughly at the same depth as ¹⁷⁷Lu, but its concentration can be significantly reduced by selecting an appropriate post-irradiation processing time, owing to its relatively short half-life. The modeling approach extended to the mapping of yields as a function of irradiation time and post-irradiation processing time. An optimized processing time window was identified. The study demonstrates that a high-energy deuteron beam can be employed to produce ¹⁷⁷Lu with high specific activity exceeding 3000 GBq/mg. The effect of different purity levels (ranging from 98% to 100%) was also discussed. The impurity levels have a slight impact. The modeling demonstrates the feasibility of obtaining ¹⁷⁷Lu with a specific activity > 3000 GBq/mg and radionuclidic purity > 99.5% when using a commercially available ¹⁷⁶Yb target of 99.6% purity.