$1.$In continuous process, recycling part of the produce effluent back to the system as feed allows to consume the unused substrate thereby increasing the yield at the expensive of equipment size. Earlier data shows that the following two equations are good estimates;

Cost $=100(\frac{R}{F}{)}^2+50,0\frac{R}{F}0\mathrm{.}5$

Yield $=\frac{0\mathrm{.}6\frac{R}{F}}{\frac{R}{F}+0\mathrm{.}3},0\frac{R}{F}0\mathrm{.}7$

Provide the reactor volume for the optimal recycle ratio, if the average residence time is $10h,$ and the feed rate is $250\frac{L}{h}.$

$5.$ For the below system, set the total and component mass balance and total energy balance for each stream,