AR$18$ The answer must be perfect. Create a diagram if needed. Strict warning: AI$-$generated content is not allowed. "Problem $13\mathrm{.}8$ Formation of lactic acid from glucose is realized in a batch reactor using Streptococcus lactis. The reactor is initially charged with $5$ L medium containing $5$ g$/$L glucose and $0\mathrm{.}1$ g$/$L cell biomass. There is no lactic acid present initially. The following information was obtained from experimental studies.

$$m $=0\mathrm{.}2$ h$-1,$ KS $=200$ mg$/$L$,$ kd $=0\mathrm{.}002$ h$-1,$ YFX$/$S $=0\mathrm{.}4$ g$-$X$/$g$-$S$,$p $=0\mathrm{.}1$g$.$

a$.$ Plot the variations of S$,$ X$,$ and P with reaction time.

b$.$ Determine the maximum production rate of lactic acid in g$/($day$-$L$)$ if with each batch a reactor loading, unloading and sterilization time of $3\mathrm{.}5$ is needed."