obs} \approx 25.2 + 2.5\log{(L_{\star}/L_{\sun})}$. This method exploits the dependence of $\Delta {\rm mag_p}$ on stellar type, but quadrature is not necessarily the ideal phase to detect exoEarths. We refer to this method as a stellar luminosity-adjusted (SLA) method. We required $\Delta {\rm mag}_{\rm obs} \le 26$ for this method as well.

### Altruistic Yield Optimization

The AYO method combines completeness and exposure time in a fundamentally different way from the methods discussed above. For each star, instead of calculating just one exposure time, we calculated an exposure time for each of the $10^5$ synthetic exoEarths simulated by our completeness calculator to achieve the assumed S/N$=10$. We then sorted the synthetic exoEarths by exposure time to obtain the completeness *as a function of exposure time* for each star. The completeness curves are then used as a metric to award exposure time to potential targets.

The top panel in Figure \[c\_vs\_t\_figure\] shows an example completeness curve for HIP 54035. This curve is similar to a vertical slice through the cumulative joint density function, as introduced by @2005ApJ...624.1010B and referred to by @2013savransky. Note that if we were to include overhead costs, they would simply be added on to the exposure time 