Three whey proteins $($A$,$ B and C$)$ are being fractionated by isocratic chromatography using a $15cm$ long cation exchange column having $90$ theoretical plates. A mobile phase flow rate of $1\mathrm{.}5mlmi{n}^{-1}$ resulted in retention times of $10,18$ and $23$ minutes respectively for proteins $A,B$ and C$.$

a$)$ Calculate resolution and comment on the feasibility of separation for all three proteins.

$10\%$

b$)$ What the length of the column should be to achieve resolution of $1\mathrm{.}5$ between peaks of proteins $A$ & B$?$ Assume that the elution volumes and the HETP value would remain the same.