In the inoculation of a fermenter in a fuel bio$-$ethanol plant, the following conditions are

required at the beginning of the fermentation:

$$ A starting yeast concentration in the fermenter of $2$ g$/$l

$$ A yeast food supplement concentration of $0\mathrm{.}08$ g$/$l

$$ A dissolved oxygen content of $16$ ppm $($mg$/$ litre$)$

The inoculum $($concentrated yeast suspension with which to seed the reactor$)$ is

available at a yeast concentration of $150$ g$/$l and has a density of $1100$kg$/$m$3$

$.$ The

working volume of the reactor is $2000$ hectolitre.

Calculate:

a$.$ The mass of yeast required to be added to the fermenter.

b$.$ The volume of inoculum required.

c$.$ The mass of inoculum required.

d$.$ The mass of yeast food added.

e$.$ The mass of oxygen added.

f$.$ The volume of this oxygen at STP in cm$3$

$.$