Consider a process with the following streams:

When \(\Delta T_{\text {min }}=10^{\circ} \mathrm{C}\), the minimum utilities for heating and cooling are \(237 \mathrm{~kW}\) and \(145 \mathrm{~kW}\), respectively, with pinch temperatures at \(110^{\circ} \mathrm{C}\) and \(100^{\circ} \mathrm{C}\). Design a HEN that satisfies the MER targets and has the minimum number of heat exchangers, \(N_{H X, \min }^{M E R}\). Show the heat duties and temperatures for each heat exchanger.

Stream Ts (C) T' (C) C (kWC) H1 350 160 3.2 H2 400 100 3 H3 110 60 8 CI 50 250 4.5 C2 70 320 100 300 23