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A process stream is cooled from T to T temperature with river water in a shell and tube heat exchanger. Contaminants in river water cause scaling problems, hence, it is needed the use of antiscaling chemical (ASC). Required antiscaling chemical amount was experimentally determined with respect to the outlet temperature of the river water as given below. Antiscaling chemical cost is $2000/kg. Pumping cost is directly proportional with the water amount delivered. Pumping cost for the river water is $1500/year for the outlet temperature of 40C. Determine the objective function, and optimum outlet temperature of river water.

process stream is cooled from T1 to T2 temperature with river water in a shell and tube heat exchanger. Contaminants in river water cause scaling problems, hence, it is needed the use of antiscaling chemical (ASC). Required antiscaling chemical amount was experimentally determined with respect to the outlet temperature of the river water as given below. Antiscaling chemical cost is $2000/kg. Pumping cost is directly proportional with the water amount delivered. Pumping cost for the river water is $1500/ year for the outlet temperature of 40C. Determine the objective function, and optimum outlet temperature of river water. \begin{tabular}{cc} \hlineTrw,out & ASC(kg/year) \\ 34 & 0.54 \\ 36 & 0.64 \\ 38 & 0.74 \\ 40 & 0.82 \\ 42 & 0.93 \\ 44 & 1.04 \\ 46 & 1.16 \\ \hline \end{tabular}