Antimicrobial resistance (AMR) is a critical global challenge driven by the evolution of bacterial populations that reduce the effectiveness of treatments. This study aims to design an optimal antimicrobial deployment strategy that minimizes both the epidemic size (epidemiological perspective) and the risk of therapeutic failure in the community (evolutionary perspective), particularly in multi-drug treatment settings. Key factors considered include compliance with recommended guidelines, infection duration, treatment initiation delay, and the effectiveness of different drugs. We evaluate the impact of introducing a new antimicrobial, conduct a sensitivity analysis of model parameters on the basic reproduction number and therapeutic failure probability, and explore outcomes of optimal treatment strategies. The approach employs a nested model that explicitly integrates within-host and between-host dynamics. At the within-host scale, the continuous character of AMR is introduced, referred to as quantitative antimicrobial resistance (qAMR). Most models addressing AMR focus on a limited number of resistant strains, often overlooking the potential continuum of resistance, especially as it develops through point mutations. The bacterial dynamics is described by an integro-differential equation, connecting this dynamics to epidemiological parameters such as individual infectiousness, disease-induced mortality, and treatment recovery rates. At the between-host scale, infected individuals are categorized into untreated, treated with compliance to treatment, and treated with non-compliance to treatment. Our results provide insights into AMR dynamics in multi-drug settings, offering a framework for optimizing treatment strategies that balance infection control and resistance prevention. This study contributes to a more effective approach for managing AMR at both individual and population levels.