help PROBLEM $3[20$ MARKS$]$

In collaboration with their R$\backslash$&D centre in Shah Alam, PROTON's Advanced Technology Division requires a helical coil compression spring optimization for their upcoming X$90$ New Energy Vehicle platform, aligning with Malaysia's National Automotive Policy and Sustainability Development Goals $($SDGs$)-7$ and $13.$ The dynamic loading parameters specify a minimum force of $25$ N at full extension and a maximum force of $95$ N at full compression. This is crucial for the lightweight, eco$-$friendly vehicle platform developed under PROTONGeely's innovative partnership initiative at Tanjung Malim manufacturing facility. The engineering specifications instruct a spring rate $\backslash (($k$)\backslash )$ of $\backslash (1850\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash )$ to achieve optimal energy recovery during suspension movement while maintaining superior ride comfort, engineered explicitly for Malaysian and ASEAN road conditions, including frequent flash floods and varied terrain. To meet the compact design philosophy of their new PROTON Intelligent Technology platform, the spring's outer diameter must not exceed $65$ mm $,$ ensuring seamless integration with the regenerative damper assembly developed in partnership with Geely. The Sapura Industrial Berhad offers wire drawing capabilities of $\backslash (2\mathrm{.}1\backslash$mathrm$\{$~mm$\},2\mathrm{.}3\backslash$mathrm$\{$~mm$\},2\mathrm{.}4\backslash$mathrm$\{$~mm$\},2\mathrm{.}6\backslash$mathrm$\{$~mm$\}\backslash ),$ and $3$ mm diameters using their newly developed eco$-$conscious suitable material. This supports Malaysia's commitment to carbon neutrality by $2050$ while meeting ASEAN's automotive sustainability standards. Following PROTON's enhanced Global Car Manufacturing Standards, the design incorporates a fatigue design factor $(\backslash ($ n j $\backslash ))$ of $1\mathrm{.}5$ to guarantee reliability throughout Malaysia's challenging tropical climate conditions, with validation through suitable fatigue$-$failure criteria. This spring design is crucial for the prototype phase of PROTON's upcoming $2025$ NEV model, supporting Malaysia's National Electric Mobility Blueprint by $2025$ while enhancing local automotive technological capabilities.