$[$OL $8\mathrm{.}21$ Modified$]$ Chemical A reacts to form R$,$ S and T according to the following reaction scheme. In this scheme, all reactions are first order:

$A{k}_{1}R{k}_{2}S$

$darr{k}_3$

$T$

where $k_1=6h^{-1},k_2=3h^{-1}$ and $k_3=1h^{-1}.$

If the feed is a solution containing A without any R$,$ S and T:

$1$

$($a$)$ What reactor $($type and size$)$ should be used to maximise the yield of R$?$ What is the product composition and $($:$\frac{c_T}{c_{A0}}\}$ from this reactor?

$($b$)$ What reactor $($type and size$)$ should be used to achieve $90\%$ of the maximum yield of S$?$