If the objective is to seek a propeller shaft that is cheap and lightweight, explore the potential of alternative materials for replacement of a mild steel (low carbon steel) with one made of aluminum alloy, magnesium alloy, and filament wound CFRP. Recognize that there must be a trade-off between mass and cost - if it is too expensive, the truck owner will not want it even if it is lighter. Explore the trade-off for two relative exchange constants: a* = 10 and for a* = 100. Material R (mm) t(mm) Mild steel (low carbon steel) 70 8 Aluminum alloy 90 10 Magnesium alloy 80 10 CFRP (carbon fiber reinforced epoxy) 100 7 HINT: Determine expression for the relative penalty function Z" and use that to rank the above potential alternative materials.