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In accordance with a public referendum held in 1980, Sweden will phase out nuclear power completely by 2010. One way to compensate for an immediate, appreciable scarcity of electric power is to construct new fossil-fuel power stations. Another is to reduce the burden on electric power by converting some end-user facilities to operate on natural gas (NG) imported from Denmark through a new pipeline to southern Sweden. We show how an optimal solution can be found for NG operation of a system incorporating an NG boiler and an electric heat pump. Electricity is priced by a time-of-use tariff (TOU) requiring a discrete optimization method. The optimal solution is characterized by the lowest life cycle cost (LCC) for the building as an energy system.