A steel plant is a complex system that is composed of interacting components. Iron-making uses a large amount of energy and emits a large amount of CO2. A strategy to decrease the energy cost and CO2, emission must consider all ways that a change in technology can affect other aspects of SP operation. To do this, a mathematical model of plants can be used for optimization. Electric arc furnace (EAF) is a process to make liquid steel (LS). An EAF makes LS by reprocessing scrap metal, direct-reduced iron, and pig iron. EAF steelmaking is an energy-intensive process, so methods to decrease energy cost are being sought. Also, the EAF sometimes uses additional carbon-based fuel and emits some CO2. A mathematical model based on material flow and energy flow is developed to simulate the EAF steelmaking and optimize the energy usage, CO2 emission or total cost. This optimization is a mixed integer linear program, and is solved by a commercial optimization tool, GAMS. Sensitivity analysis that considers the costs of electricity and natural gas is added to anticipate how optimization results can change with as variables change. The effects of carbon tax are also considered. Using this mathematical model, case studies are conducted, and optimization results are evaluated. The results of this study give an optimized strategy for steelmaking, while maintaining steel grade; the strategy can increase the efficiency of the steelmaking process.