Bacteria $($Pseudomonas sp$.)$ are grown in an $8\mathrm{.}0$ L CSTR$/$chemostat on limiting substrate, acetate. The cells are growing

in the exponential growth phase with a mass doubling time of $2\mathrm{.}33$ hours. The saturation constant $(K_s)$ is $1\mathrm{.}65$

$\frac{g}{L},$ and cell yield on acetate is $0\mathrm{.}41g$ cell $\frac{?}{g}$ acetate. If a chemostat is operated with a sterile feed stream

containing $38\mathrm{.}2\frac{g}{L}$ acetate $($and the rest of the nutrients supplied in excess$),$ find the following:

A$.$ the specific growth rate during exponential growth $({}_{\text{m}\text{a}\text{x}})dots$ which equals the maximum dilution rate $(D_{\text{m}\text{a}\text{x}})$

B$.$ the steady state substrate concentration in the CSTR when the dilution rate is $0\mathrm{.}5D_{\text{m}\text{a}\text{x}},0\mathrm{.}8D_{\text{m}\text{a}\text{x}},$ and $0\mathrm{.}9D_{\text{m}\text{a}\text{x}}$

C$.$ the steady state cell concentration when the dilution rate is half of the maximum $(D_{\text{m}\text{a}\text{x}}),0\mathrm{.}8D_{\text{m}\text{a}\text{x}},$ and $0\mathrm{.}9D_{\text{m}\text{a}\text{x}}$

D$.$ the rate of cell production DX $($gdw cells$/$L$-$h$)$ and total cell production rate FX $($gdw cells$/$h$)$ when operated at

$0\mathrm{.}5D_{\text{m}\text{a}\text{x}},0\mathrm{.}8D_{\text{m}\text{a}\text{x}},$ and $0\mathrm{.}9D_{\text{m}\text{a}\text{x}}.$

E$.$ Calculate $D_{\text{o}\text{p}\text{t}}($optimum dilution rate to maximize cell production$)$ and the total cell production rate at this

optimal dilution rate. Discuss your answers to parts C$,$ D & E$.$ Do they make sense?