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This research deals with making a mathematical model for the design of a dual system for hot water production for industrial purposes as well as cooling using an ejector at a determined operating conditions, by utilizing dissipated thermal energy from a steam boiler and for a cooling capacity of (15) KW. For the system simulation, mathematical relations were presented for each component which were then combined together and programmed using (matlab) version 6.5 to optimize the system performance and design the components at this situation, using refrigerant (R-123) as the working fluid because of it's good characteristics and relatively high efficiency after a comparison study with other suitable refrigerants to be used for this system. Satisfactory results were obtained having good agreement with previous researches and a COP value of (0.667). The results show a suitable size of the designed system such that it can be used in a wide range of cooling and hot water production purposes. Also, the effect of operating conditions variation on the quantity and temperature of hot water and system performance were studied. [ABSTRACT FROM AUTHOR]