Plasmonic nanostructures made from Earth abundant and low-cost metals have recently emerged as a potential alternative to typical noble plasmonic metals. Here we report a quantum mechanical study of the optical response evolution of bi-metallic core-shell nanorods made of simple-metals Mg, Al and Na atoms. We base our calculations on the computationally efficient time-dependent density-functional theory. We find that core-shell nanorods show rich and enhanced optical properties in comparison to pristine nanorods as a result of the interface formed between the core and the shell regions. Perhaps the most interesting result from our calculation is the dramatic spectral intensity enhancements in the case of core-shell nanorods. We believe that our findings will be helpful in the design of plasmonic devices based on core-shell nanorods made of simple metals.