Q $2.$ An enzyme is used to convert substrate to a commercial product in a $1600-$litre batch reactor. V$\_$max for the enzyme is $0\mathrm{.}9$g $/$ l $.$ h ; K$\_$m is $1\mathrm{.}5$g $/$ l$.$ Substrate concentration at the start of the reaction is $3$g $/$ l; according to the stoichiometry of the reaction, conversion of $1$g substrate produces $1\mathrm{.}2$g product. The cost of operating the reactor including labour, maintenance, energy and other utilities is estimated at $ $4800$ per day. The cost of recovering the product depends on the extent of substrate conversion and the resulting concentration of product in the final reaction mixture. For conversions between $70\%$ and $100\%,$ the cost of downstream processing can be approximated using the equation:

C$=155-0\mathrm{.}33$ X

where C is cost in $ per kg product treated and X is the percentage substrate conversion. The market price for the product is $ $750$kg$^-1.$ Currently, the enzyme reactor is operated with $75\%$ substrate conversion; however, it is proposed to increase this to $90\%.$ Estimate the effect this will have on the economics of the process. $(30$ pts$)$