$(20$ pts$)$ You are running a fermentation in a reactor with a known maximum kLa of $100$

hr$-1.$ You have also done experiments to determine the specific respiratory rate of your

strain during growth and product formation to be $10$ mmoles O$2/($gram cells$*$hr$).$ Finally,

you know the specific growth rate of your strain to be $0\mathrm{.}3$ hr$-1.$ Assuming the saturation

concentration of oxygen in your media to be $7$ mg$/$L under the conditions in the fermenter.

a$.$ What is the maximum cell density that this reactor can support $(4$ points$)?$ Hint:

unit conversions will be necessar