Design of a non$-$limiting medium. You are designing a culture medium for CHO cells that requires the addition of a growth factor, F$.$ You are given the following information:

The affinity constant of $F,K_F,$ in this system is $0\mathrm{.}05\frac{g}{L}.$

The production of $1g$ of biomass consumes $0\mathrm{.}2g$ of $F.$

$F$ is non$-$limiting when its concentration is $10K.$

a$.$ In your process, the initial biomass concentration is $2\frac{g}{L}$ and the final biomass concentration is $10\frac{g}{L}.$ How many grams of $F$ should be added to $100L$ of culture to keep F non$-$limiting during the entire process?

b$.$ During your process in Part $($a$),$ how many grams of $F$ is left in the culture when the biomass concentration is $5\frac{g}{L}?$