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Problems                                                            435



                  8.C.2. From the substrate conversion rate data, we would like to design a CSTR bioreactor
                  by choosing the inlet substrate conversion and inlet volumetric flow rate, within the limits
                                                         l          l
                                     0M ≤ [S] 0 ≤ 2M  0     ≤ υ ≤ 1                 (8.246)
                                                        min        min
                  that maximize the conversion rate in the bioreactor. If the uncertainty in the parameter values
                  is not too great, we get a reasonable design by simply using the most probable parameter
                  values. However, this approach completely neglects the uncertainty in the parameters them-
                  selves. Using statistical decision theory, compute the optimal inlet substrate concentration
                  and inlet flow rate, taking into account the effect of uncertainty.
                  8.C.3. Using the single-response data of Table 8.5 for the enzymatic substrate conversion
                  reaction, compute the Bayes factor for comparing the following models: (1) Michaelis–
                  Menten kinetics with substrate inhibition and (2) Michelis–Menten kinetics with no sub-
                  strate inhibition. Do the data strongly suggest that substrate inhibition is significant for this
                  system?
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