A CSTR $($turbidostat$)$ bioreactor uses Streptococcus lactis to produce lactic acid $($product$)$ from glucose $($substrate$).$

Assume sterile feed and operation at steady state.

Given:

$S_o=5\mathrm{.}0\frac{g}{L}$

$Y_{\frac{x}{s}}^M=0\mathrm{.}40g\frac{x}{g}S$

${}_{\text{m}\text{a}\text{x}}=0\mathrm{.}2h^{-1}$

$Y_{\frac{P}{S}}=0\mathrm{.}2g\frac{P}{g}S$

$K_S=200m\frac{g}{L}$

$q_P=0\mathrm{.}1g\frac{P}{g}x-h$

$k_d=0\mathrm{.}002h^{-1}$

A$.$ Make a plot showing how $S$

$P$ and $x($all on the same plot$)$ vary with dilution rate, $D,$ to a point above

wash$-$out.

$\{$A spreadsheet will be helpful here; calculate values for $S,P$ and $x$ for different values of $D,$ starting at $0$

and continuing until you go above washout$\}$

B$.$ Make another plot showing how DX and DP $($rates of production of cells and product$)$ vary with D $($on the

same graph$),$ covering the same range of dilution rates in $A.$

C$.$ Briefly discuss the optimal dilution rate needed to maximize product concentration in the reactor and exit

stream $($graph A$)$ and the optimal dilution rate needed to maximize the rate of production of the

product $($graph B$).$