Lactobacillus casi is propagated under essentially anaerobic conditions to provide a starter culture for manufacturing Swiss cheese. The culture produces lactic acid as a by$-$product of endogenous metabolism. The growth parameters are given by $Y_{\frac{x}{S}}=0\mathrm{.}23gx(gS{)}^{-1},K_S=0\mathrm{.}15\frac{g}{L},max=0\mathrm{.}33h^{-1},K_d-0\mathrm{.}03h^{-1}.$ A stirred$-$tank fermentor is operated in fed$-$batch mode at pseudo$-$steady state with a feed flow of $4000\frac{L}{h}$ and feed substrate concentration of $80\frac{g}{L}.$ The feed is started such that pseudo$-$steady state is reached from time zero. After $8h,$ the liquid volume is $40,000L.($Hint: consider which type of fed$-$batch reaction this is$.)$

The initial culture volume is $8000$L$.$

Question:

What is the substrate concentration in the reactor after $8h$ fed$-$batch operation in $\frac{g}{L}?$