Propelled by the weakness of some notable scientific investigations and the continual desire to achieve a more precised result for the eradication of dual HIV-pathogen infections, the present paper formulated a 7-Dimensional nonlinear mathematical dynamic model presupposed to account for the optimal treatment of asymptomatic dual HIV-pathogen infections studied under quadrupled treatment functions. The model was presented as a linear optimal control time problem (LOCTP) analyzed using linear programing approximability approach, embedded with theoretical measured space. The study as well established the positivity and boundedness of model state variables and numerical simulations conducted. Results of simulations clearly raises positive variations in comparison of healthy CD4⁺ T lymphocytes count, dual HIVpathogen infections, critical role of dual CTLs and the aggressiveness of virions before and after the introduction of multiple chemotherapy treatment. Therefore, in justifying the application of linear programing approximation model, the study strongly advocates the articulation of delay intracellular into the state variables for enhancement of future investigation.