Two heat exchangers in a circulating water loop, as shown in Fig. 7-4, transfer heat from a fluid condensing at 80°C to a fluid boiling at 20°C. The required rate of heat transfer is 65 kW, the U value of both heat exchangers is 0.03 kW/(m² K), the first cost of the heat exchangers is $80/m² of heat- transfer area, and the present worth of the lifetime pumping cost in dollars is 12,000w. Develop the objective function for the total present cost of the system along with any constraint equation(s). 80°C vapor wwwww 20°C vapor 12 w kg/s water, cp = 4.19 A₁, m² Heat exchanger 1 11 80°C liquid wwwww wwwww A2. m² Heat exchanger 2 FIGURE 7-4 Heat-exchange loop in Prob. 7.2. 20°C liquid