$(5$ pts$)$ A strain of yeast is being cultivated in a $30-L$ CSTF with a cell recycling system $9$cell

settler$)$ as shown in the flowing figure. The cell settler was designed so that the cell

concentration of its outlet stream is $30\%$ of that of its inlet stream, whereas the substrat

concentrations of the two streams are the same. The growth rate of the cells can be represented

by the Monod kinetics with the parameters ${}_{\text{m}\text{a}\text{x}}=0\mathrm{.}3h{r}^{-1},K_S=0\mathrm{.}05\frac{g}{L},$ and $Y_{\frac{x}{s}}=$

$0\mathrm{.}025\frac{g}{g}.$ The inlet substrate concentration is $100\frac{g}{L}$ and the flow rate is $20\frac{L}{h}r.$ The feed

stream is sterile. Calculate the steady$-$state substrate and cell concentrations in the fermenter.