In a sequential two$-$stage chemostat configuration, the first and second reactors possess volumes of $V_1=800$ liters and $V_2=500$ liters, respectively. The primary reactor is designated for the cultivation of biomass, while the secondary reactor focuses on the production of a specific secondary metabolite. The influent stream to the initial reactor has a flow rate of $F=100$ liters per hour, with a glucose concentration of $S=7\mathrm{.}0$ grams per liter. Apply the following kinetic parameters for the cellular processes: ${}_m=0\mathrm{.}5h^{-1}$ and $K_S=0\mathrm{.}1\frac{g}{l}.[$take: $Y_{\frac{x}{s}}=0\mathrm{.}4gdw$ cells $\frac{?}{g}$ glucose$](6$ Marks$)$

a$.$ Determine cell and glucose concentrations in the effluent of the first stage.

b$.$ Assume that growth is negligible in the second stage and the specific rate of