The attainable region (AR) technique is used to find the optimum process design for an exothermic reversible reaction system where allowance is made for external cooling using two different constant temperature utilities. Heat exchange with the two utilities has different associated costs. The general optimum process structure (equipment) for the specified system was obtained via finding the attainable region. The temperature progression required for the exothermic reversible reaction was obtained by a sequence of structures. The hot reaction mixture was adiabatically reacted in a CSTR followed by a plug now reactor then cooled down in a differential cold shot converter. This was followed with external cooling of the reactor, firstly with the hotter utility and then with the colder and more expensive utility. The optimum control of the cold shot cooling as well as the external cooling was determined using the AR technique.