Hello, i need help with this exercise. I need every step of the procedure for every point (required the program polymath).

The kinetics for the enzymatic conversion of a substrate S is described by the Michaelis-Menten equation whose values of the parameters Km and Vmax are equal to 0.025 mol/L and 0.05 mol/(L * min), respectively. Suppose we want to achieve 90% substrate conversion using a continuous bioreactor:

1. The bioreactor is fed with a concentration of S equal to 0.35 mol/L. Determine the residence time in case a perfect mixing reactor is used and in case a plug flow bioreactor is used;
2. For which values of the kinetic parameters are the residence times for the two bioreactors similar?
3. Determine the time profile of the substrate concentration in the case in which the operating conditions are those indicated in point a) and the volume of the bioreactor & perfect mixing is equal to 750 L. It is assumed that the concentration of the substrate al inside the bioreactor is negligible at the start of feeding (Use polymath).
4. Determine the spatial profile of the substrate conversion in the case in which the operating conditions are those indicated in point a) and the volume of the plug-flow bioreactor is equal to 750 L Use polymath)