It was shown in an earlier work by us that entropy generation and energy (hot utility or cold utility) consumption of isothermal, isobaric reactor networks depend only on the network's inlet and outlet stream compositions and flow rates and are not dependent on the reactor network structure, as long as the universe of realizable reactor units and network outlet mixing units are either all endothermic interacting with a single hot reservoir, or all exothermic interacting with a single cold reservoir, respectively. It is shown that when the universe of realizable reactor/mixer units, of isothermal, isobaric, continuous stirred tank reactor networks, consists of both endothermic units interacting with a single hot reservoir and exothermic units interacting with a single cold reservoir, the network's net (hot minus cold) utility consumption depends only on the network's inlet and outlet stream compositions and flow rates (and does not depend on the network's structure). In contrast, the network's entropy generation depends on the network's inlet and outlet stream compositions and flow rates, and the network's hot utility (or cold utility) consumption. The latter, in general, depends on the network structure, thus making entropy generation also, in general, depend on network structure. Thus, the synthesis of isothermal, isobaric reactor networks, with fixed inlet and outlet stream specifications, is equivalent to the synthesis of minimum hot (or cold) utility consuming such networks. The Infinite DimEnsionAl State-space conceptual framework is used for the problem's mathematical formulation, which is then used to rigorously establish the above equivalence. A case study involving Trambouze kinetics demonstrates the findings. (c) 2014 American Institute of Chemical Engineers AIChE J, 61: 103-117, 2015