\[\frac{\partial \pi_{i}}{\partial q_{i}} = a - (b_{1}q_{1} + \dots + b_{n}q_{n}) - b_{i}q_{i} = 0\]
\[na - n(b_{1}q_{1} + \dots + b_{n}q_{n}) = b_{1}q_{1} + \dots + b_{n}q_{n}\]
\[
n = \frac{b_{1}q_{1} + \dots + b_{n}q_{n}}{a - (b_{1}q_{1} + \dots + b_{n}q_{n})}
\]