In a continuous bio-reactor (or fermenter), the volumetric flow rate of feed to the fermenter is q(L/h). The liquid volume is constant V(L). The cell concentration of the feed and out of the fermenter are X0 and X(g/L), respectively. While the substrate concentration in and out of the fermenter are S0 and S(g/L), respectively. The growth rate of cells is X(g/Lh) and the consumption rate of substrate is kX. Here, the constant k=1.2 is the inverse yield of substrate to cell mass. The cell death rate is neglected. The specific growth rate is a function of the substrate concentration. a) Set up a dynamic model of the continuous stirred reactor describing the cell and substrate concentrations. b) Simulate concentration of cells and substrate as function of time when the specific growth rate is =S+32S(1/h) and q/V=0.5(1/h) with S0=4.0g/L and X0=0.01 g/L and starting with no cells and substrate in the reactor. c) Reduce the model by assuming steady-state conditions and negligible feed of cell mass to the reactor. Calculate the steady-state condentrations