One large scale fermentation tank holds about $15,850$ gallons $(600$ hL$)$ of

beer during the fermentation process, which lasts about $3$ weeks on average. On average,$0\mathrm{.}41$ kg of CO$2$ is produced for every liter of beer. You are tasked with determining the production rate for filling CO$2$ cylinders $($cylinders$/$h$)$ for one fermenter. Since the CO$2$ is produced as an off gas, you need to determine:

a$.$ The volumetric flow rate $($L$/$h$)$ that will feed the compressor$/$cooling$/$distillation system that will liquify the CO$2$ and enable filling the gas which holds $50$ lbs$.$ net weight of liquid CO$2.$ The fermentation process operates at $20$C and $1$ Atm and the density of liquid CO$2$ is about $0\mathrm{.}827$ g$/$ml$.$

b$.$ The number of cylinders that can be filled per hour while the fermentation process is running.