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Integrated Energy System Problem represents variety of commonly used energy systems in buildings, cars or even small-scale power grid networks. In this paper, we use linear programming to formulate an Integrated Energy System Problem that minimizes total cost of energy system while satisfying operational constraints such as energy generation capacity, saving capacity and users demands. This model is completely flexible to changes in demand and energy price over time. It also has the ability to deal with energy shortage or energy surplus in different time periods. We also develop a multi-objective optimization, considering total cost and environmental impact, for above energy model and discuss a numerical example for multi-objective model.