Industrial Bioreactor Output Bottlenecks (Chemical Engineering)

In an automated biochemical fermentation facility, process engineers monitor the production rate $V([S])$ (in kilograms of synthetic protein per hour) inside a continuous stirred-tank bioreactor. The reaction velocity follows a Michaelis-Menten saturation profile modeled as a function of the input substrate nutrient concentration $[S]$ (in millimoles per liter):

To optimize facility capital investment and feedstock supply logistics, the plant management team needs to determine the theoretical maximum production bottleneck ($V_{\max}$) when the reactor is supplied with an unbounded excess of substrate ($[S] \to \infty$).

1. Identify the highest powers of $[S]$ in the numerator and denominator to determine the growth dominance regime.
2. Evaluate the limit analytically:
   $$\lim_{[S] \to \infty} \frac{450[S]}{18 + [S]}$$
3. State the horizontal asymptote equation and its practical meaning for biochemical throughput.