The chemostat growth of a microorganism on glucose gave a cell production

rate of:

$q_x=\frac{4}{3}\frac{Sx}{S+4}\frac{\text{g}\text{c}\text{e}\text{l}\text{l}\text{s}}{m^2(h)}$ and cell yield coefficient $of{Y}_{\frac{x}{S}}=0\mathrm{.}1g{g}^{-1}.$

For a chemostat volume of $1m^3$ and feed glucose concentration of $60g{m}^{-3},$

$($a$)$ calculate the feed flow rate for which maximum cell production rate is

obtained. What is this maximum cell production rate?

$($b$)$ calculate the largest feed flow which can be handled in the given reactor.

$($c$)$ A centrifuge is installed, and a fraction, $$ of the cells is returned to the

reactor. Determine the recirculation rate, $R$ as a function of $$ if the

specific growth rate of the cells is the same as that found in $($a$)$ is to be

maintained, and the feed flow rate is $2\mathrm{.}5m^3{h}^{-1}.$ Hence determine the

minimum $.$