A binary mixture with a relative volatility of $2$ is to be separated in process that has two flash drums hooked together. The feed is an $100$kmo$\frac{l}{h}$ of an equimolar mixture. In the first flash drum, $50\%$ of the feed entering the unit is vapourized. The liquid from this flash drum is heated and flashed in a second drum. The vapour product from flash drum $2$ contains $50\%$ of the more volatile component. Based on this information and answer the following:

$($a$)$ Draw a sketch of the process.

$($b$)$ Write down the operating line equations of both the flash drums and show them on the $y-x$ diagram.

$($c$)$ Calculate the flow rates and compositions of all the product streams and list them in a stream table.