Design a HEN to meet the MER targets for \(\Delta T_{\text {min }}=10^{\circ} \mathrm{C}\) and \(N_{H X, \text { min }}\) for a process involving five hot streams and one cold stream as introduced by Yee and Grossmann (1990):

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Stream T' (K) T' (K) C (kW/K) HI 500 320 H2 480 380 H3 460 360 H4 380 360 20 H5 380 320 12 C1 290 670 646828 18