The renewable energy transition requires energy storage technologies for grid-balancing and transportation. Lithium-ion batteries have been widely adopted for these applications, but supply risks due to geopolitical tensions have motivated the search for alternative chemistries less dependent on critical raw materials. Sodium-ion batteries have garnered notable attention as promising post-lithium chemistry due to the relative abundance of sodium and its similar manufacturing process to lithium-ion batteries. This work estimated the cost of producing sodium-ion battery packs from cells optimized via multiphysics modeling for energy or power-based applications. This study replicated a multiphysics model of a pouch format sodium-ion battery from literature in COMSOL Multiphysics®. This model determined the optimal active material used in batteries under 0.1C to 10C discharge rates to maximize the energy density. The cost of battery packs produced from the optimized cells was then determined using the Battery Performance and Cost (BatPaC) model of Argonne National Laboratory, which considers material and manufacturing costs. The optimization results reveal that energy cells have thicker electrodes and lower porosities (217 µm thick 0.11 porosity anode, 237 µm thick 0.10 porosity cathode for 0.1C), which maximize the amount of active material per unit mass. Power cells have thinner electrodes and larger porosities to minimize electrical resistance (58 µm thick 0.32 porosity anode, 63 µm thick 0.31 porosity cathode for 10C), reducing energy losses at high currents. Moreover, we compared the calculated production cost for energy and power applications for sodium-ion batteries, highlighting essential parameters affecting the price. The model observed a 26.42% increase in total material cost per kWh when transitioning from energy to power cells. The model may also be refined by considering sodium-ion batteries with different cathode and anode chemistries in different formats and their applications in different use cases.