The synthesis problem of energy supply systems includes the selection of proper heating and power generating units as well as energy integration. Such problems have been generally formulated as a linear programming (LP) problem. The structural analysis of the problem and solutions is focussed on rather than merely solved. As a practical consideration for preliminary selection of technologies, a problem regarding the selection of heating devices such as electric heaters, furnaces, steam heaters, or heaters with a heating medium under given loads is defined as a synthesis problem of optimal heat and power supply systems and formulated into an LP form with an objective function of minimum fuel. The results of analysis of the LP problem clarify essential structures of heat and power supply systems under arbitrary heat and power demands.