Reactant A is decomposed as follows:

A$->$R$->$S $,$ with k$1=0\mathrm{.}1$ min$-1,$ k$2=0\mathrm{.}1$ min$-1,$ E$1/$R $=15,000$K and E$2/$R $=8,000$K$.$ R is the desired product and S is unwanted. R is to be obtained from $15$ L$/$min of pure feed in A at a concentration of $1$ mol$/$L$.$

a$)$ Recommend a suitable temperature and reaction system for the production of R$.$ Justify.

b$)$ Calculate the volume of a PFR reactor that maximizes the exit molar flow of R$.$ At these optimal conditions, calculate the overall efficiency $($YR$).$