$18\mathrm{.}27($A$)($SI units$)$ An L$-$shaped structural section is direct extruded from an aluminum alloy billet whose length $=500mm$ and diameter $=100mm.$ Dimensions of the extruded cross section are given in Figure P$18\mathrm{.}27.$ The strength coefficient and strain$-$hardening exponent of the aluminum alloy are $240$ MPa and $0\mathrm{.}15,$ respectively $($Table $3\mathrm{.}4).$ The die angle $=90,$ and the Johnson strain equation has constants $a=0\mathrm{.}8$ and $b=1\mathrm{.}5.$ Determine the $($a$)$ extrusion ratio, $($b$)$ shape factor, and $($c$)$ length of the extruded section if the butt remaining in the container at the end of the ram stroke is $25$ mm long. $($d$)$ Compute the maximum force required to drive the ram forward at the start of extrusion.