Consider the plots on the next page showing the substrate $($S$),$ cell dry weight $($X$),$ and

secreted extracellular product $(P)$ concentrations as a function of time during batch culture of

yeast $Y1,$ which was inoculated at a concentration $x(0)=0\mathrm{.}5g\frac{x}{L}$ at $t=0h.$ The

information in these plots will be used to design a CSTR to produce P$.$ The feed medium and

operating conditions $(T,pH,DO,$ etc.$)$ will be the same as those used in the batch culture.

a$.$ If the outlet yeast $Y1$ concentration is to be maintained at $x=30gx{L}^{-1},$ determine the

reactor volume that would be required to process a feed flow rate, $F=1000L{h}^{-1}.$

b$.$ Determine the following parameters for the CSTR system:

$($i$)$ The product concentration, $P,$ in the reactor outlet stream

$($ii$)$ The volumetric production rate of product $(gP{L}^{-1}{h}^{-1})$

$($iii$)$The specific product formation rate, $q_P$

c$.$ Now consider the yields from substrate in the CSTR:

$($i$)$ Determine the apparent yield of product from substrate, ${?}^{\text{a}\text{p}\text{p}}{Y}_{\frac{P}{s}}$

$($ii$)$ Determine the apparent yield of yeast from substrate, app $Y_{\frac{x}{S}}$

$($iii$)$Consider the individual theoretical maximum values for the yield of $x$ from $S$

${(}^M{Y}_{\frac{x}{S}})$ and the yield of $P$ from $S{(}^M{Y}_{\frac{P}{S}}).$ Briefly discuss whether you would

expect ${?}_{\frac{x}{S}}^{M^M}$ and ${?}^{M_Y}{Y}_{\frac{P}{S}}$ to be slightly greater or substantially greater

$(>25\%)$ than the respective apparent yields $({?}^{\text{a}\text{p}\text{p}}{Y}_{\frac{x}{S}}$ and ${?}^{\text{a}\text{p}\text{p}}{Y}_{\frac{P}{S}})$ you calculated in

part $($b$).$ Be sure to explain your reasoning.

Be sure to show $($including on the plot$)$ and clearly explain your work for all parts of the

problem.