From eq. 21 in the manuscript
\[ E_\alpha\left(b, r\right) = \dfrac{1}{\log\left(r\right)} \dfrac{M_0}{1 - e^{-\frac{b}{r}}} \left(\alpha b + 1 - \alpha\right) \]
Cost function parameter \(\alpha\) determines the balance between the number of PCR reactions per day vs. lower enrichment rates i.e. more days required to reach target recombinant frequency.