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Biomass is being produced in a continuous stirred tank bioreactor of $750$ L capacity. The sterile feed containing $8 \: g \cdot L^{-1}$ glucose as substrate was fed at a flow rate of $150 \: L \cdot h^{-1}$. The microbial system follows Monod’s model with $\mu m = 0.4 \: h^{-1}$, $K_s = 1.5 \: g \cdot L^{-1}$ and $Y_{x/s} = 0.5 \:g$, cell $\text{mass }\cdot g$ substrate$^{-1}$. Determine the cell productivity $(g \cdot L^{-1} \cdot h^{-1})$ at steady state.

- $0.85$
- $0.65$
- $0.45$
- $0.25$