You have a $\backslash (40\backslash$mathrm$\{$~mm$\}\backslash$times $8\backslash$mathrm$\{$~mm$\}\backslash )$ cross$-$section low carbon steel billet available $($the length can be cut to size as needed$)$ and your company possesses equipment with the following capabilities: $\backslash (\backslash$square $\backslash )$

$1.$ Hot open die forging $\backslash ((\backslash$mathrm$\{$MF$\}=2)\backslash )$

$2.$ Hot closed die forging $\backslash ((\backslash$mathrm$\{$MF$\}=5)\backslash )$

$3.$ Hot impression die forging $\backslash (($M F$=9)\backslash )$

$4.$ Cold open die forging $\backslash ((\backslash$mathrm$\{$MF$\}=1\mathrm{.}5)\backslash )$

$5.$ Cold closed die forging $\backslash ((\backslash$mathrm$\{$MF$\}=4)\backslash )$

$6.$ Cold impression die forging $\backslash ((\backslash$mathrm$\{$MF$\}=7)\backslash )$

a$)$ Select a process from the list above for the manufacture of the component shown in Figure $1$ on page $2!$ There is no requirement for the surface finish and the design allows relatively large tolerances. $(3$ pts$)$

b$)$ To what length would you cut the blanks for forging? $(4$ pts$)$

c$)$ Calculate the required forging force! Material parameters and a list of equations are provided in the appendix. $(5$ pts$)$

d$)$ Indicate $1$ method to reduce the forging force requirement! $(2$ pts$)$