A liquid reaction with an assumed rate $r_A=-k{C}_A$ is taking place at constant temperature and pressure in a series of reactors, the Levenspiel plot for this reaction is shown below. Pure A enters the reactor at $FA0=1000\frac{\text{m}\text{o}\text{l}}{s},C{A}_0=2\frac{\text{m}\text{o}\text{l}}{L}.k_A=2(\frac{1}{s}).$

a$)$ Select a series of reactors $($CSTRs and PRFs$)$ and design a sequence to minimize the total volume to achieve $90\%$ conversion with the Levenspiel plot. Please shade the area for each reactor you choose on the plot directly.

b$)$ Determine the volumes for the reactors in your series.