In this paper, we give a simple mathematical model for a multi‐drug antimicrobial resistance. The model describes the dynamics of the susceptible and three classes of infected populations. The first class of the infected society is sensitive to the first antimicrobial drug but resisted to the second drug. The other infected community responds to the second antimicrobial drug but resistant to the first drug, and the third class shows resistance to both of the two drugs. The stability conditions of the multi‐drug antimicrobial resistance equilibrium states are derived. Also, we illustrated the analytical results by some numerical simulations. Finally, we used the multiobjective optimization approach to find the minimum doses of antimicrobial drugs.