Phase diagram

$2.$ Consider the hypothetical eutectic phase diagram for metals A and B $,$ which is similar to that for the leadtin system, see the following figure as an example. Assume that: $($I$)\backslash (\backslash$alpha $\backslash )$ and $\backslash (\backslash$beta $\backslash )$ phases exist at the $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ extremities of the phase diagram, respectively; $(2)$ the eutectic composition is $\backslash (35$ w t $\backslash \%\backslash$mathrm$\{$~A$\}-65\backslash$mathrm$\{$wt$\}\backslash \%\backslash$mathrm$\{$~B$\}\backslash )$; and $(3)$ the composition of the $\backslash (\backslash$alpha $\backslash )$ phase at the eutectic temperature is $\backslash (85$ w t $\backslash \%\backslash )$ A$-15$ wt$\backslash \%$ B$.(20$ points$)$

$($a$)$ Determine the composition of an alloy that will yield primary $\backslash (\backslash$beta $\backslash )$ and $\backslash (\backslash$beta $\backslash )$ total mass fractions of $0\mathrm{.}37$ and $0\mathrm{.}75,$ respectively.

$($b$)$ Suggest what composition range can provide a precipitation hardening alloy? briefly explain your rationale.