$2.(\backslash (\backslash$mathbf$\{18\}\backslash )$ pts total$)$ From the $\backslash (\backslash$mathrm$\{$Fe$\}^\{-\}\backslash$mathrm$\{$Fe$\}\_\{3\}\backslash$mathrm$\{$C$\}\backslash )$ phase diagram below, answer the following questions.

$($a$)(4$ pts$)$ According to the above phase diagram, what is the possible range for carbon composition that can make i$)$ steels and ii$)$ cast irons.

$($b$)(4$ pts$)$ Write the peritectic reaction found in this phase diagram. Which manufacturing process is governed by this reaction? please provide a detailed explanation for each step

$($c$)(4$ pts $)$ Consider an alloy containing $\backslash (0\mathrm{.}9\backslash$mathrm$\{$wt$\}\backslash \%\backslash$mathrm$\{$C$\}\backslash ),$ solidified to room temperature from the melt. What is $($are$)$ the phase$($s$)$ present in its resulting microstructure.

$($d$)(6$ pts$\backslash ()\backslash )$ At $\backslash (800^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $\backslash (1\mathrm{.}5\backslash$mathrm$\{$wt$\}\backslash \%\backslash$mathrm$\{$C$\}\backslash ),$ what is $($are$)$ the equilibrium phase$($s$)?$ Identify the composition and the relative amount of each phase.