A binary mixture containing $48$ mass $\%$A and $B$ is to be separated in a plant containing of two stages distillation process. The bottom product from the first distillation column is used as the feed to the second column. The mass composition in percentage of $B$ in the overhead product from the first distillation column is to be $5\%.$ The overhead product from the second column is to contain $98$ mass $\%$ of A$.$ The bottom product from the second column contain $1\%$ A$.$ The fresh feed enters the plant at a rate of $10000k\frac{g}{h}$ and the overhead product from the second column exits at a rate of $2000k\frac{g}{h}.$

$4\mathrm{.}1.$ Draw and completely label the schematic diagram of the process.

$4\mathrm{.}2.$ Calculate all the unknown flow rates and mass compositions of the process stream.