Step 1: Use the statutory ventilation requirements.
The minimum quantity of air is taken as the greater of:
\[
6\ \mathrm{m^3/min}
\]
per person, or
\[
2.5\ \mathrm{m^3/min}
\]
per tonne of daily production.
Step 2: Calculate both values.
For \(150\) workers,
\[
Q_1=150\times6=900\ \mathrm{m^3/min}.
\]
For \(500\) t/day production,
\[
Q_2=500\times2.5=1250\ \mathrm{m^3/min}.
\]
Since the larger value is adopted,
\[
Q=1250\ \mathrm{m^3/min}.
\]
Therefore,
\[
\boxed{(C)}
\]
is the correct answer.