Species interactions are crucial in ecosystems, but competition can sometimes prevail over mutualism, leading to various implications and outcomes. However, the transition from mutualism to competition has yet to be experimentally explored. This research examines the mutualism between cross-feeding bacteria strains that provide essential amino acids to their partner when both strains are exposed to antimicrobials. The strains exhibit extinction, mutualism, or competition without antimicrobials, depending on the freely available amino acid levels. The behavior of both species is influenced by resource availability. When the strains are exposed to antimicrobials, population dynamics are dependent on the proportion of bacteria resistant to the antimicrobial, with low resource levels leading to the extinction of both strains. However, high resource levels lead to continued competition between both strains. In order to reduce the proportion of resistant bacteria, an optimal control problem is formulated, revealing that cooperation leads to immediate control of both sensitive and resistant strains. In contrast, competition only reduces the density of one of the strains. Parameter estimation was performed using data collected from laboratory experiments with E. coli bacteria to fit the mathematical model to the experimental data.