Consider a three-stage heat exchanger optimal design problem [1, 2]. A cold fluid is heated from 100 °F to 500 °F by passing through three heat exchangers in series (labeled , , and in the diagram). At each stage, the cold stream is heated by a hot fluid. You can set the temperatures (expressed in °F) of the hot fluids entering the three heat exchangers. The overall heat transfer coefficients (expressed in Btu/hr ºF) of these exchangers are equal to , , and . Assume that the hot and cold fluids have the same flow rate and specific heat , and that Btu/hr ºF.