jats:titleAbstract</jats:title> jats:pThe jats:italicWide Field InfraRed Survey Telescope</jats:italic> (jats:italicWFIRST</jats:italic>) was the highest-ranked large space-based mission of the 2010 jats:italicNew Worlds</jats:italic>, jats:italicNew Horizons</jats:italic> decadal survey. It is now a NASA mission in formulation with a planned launch in the mid 2020s. A primary mission objective is to precisely constrain the nature of dark energy through multiple probes, including Type Ia supernovae (SN Ia). Here, we present the first realistic simulations of the jats:italicWFIRST</jats:italic> SN survey based on current hardware specifications and using open-source tools. We simulate SN light curves and spectra as viewed by the jats:italicWFIRST</jats:italic> wide-field channel (WFC) imager and integral field channel (IFC) spectrometer, respectively. We examine 11 survey strategies with different time allocations between the WFC and IFC, two of which are based upon the strategy described by the jats:italicWFIRST</jats:italic> Science Definition Team, which measures SN distances exclusively from IFC data. We propagate statistical and, crucially, systematic uncertainties to predict the Dark Energy Task Force figure of merit (FoM) for each strategy. Of the strategies investigated, we find the most successful to be WFC focused. However, further work in constraining systematics is required to fully optimize the use of the IFC. Even without improvements to other cosmological probes, the jats:italicWFIRST</jats:italic> SN survey has the potential to increase the FoM by more than an order of magnitude from the current values. Although the survey strategies presented here have not been fully optimized, these initial investigations are an important step in the development of the final hardware design and implementation of the jats:italicWFIRST</jats:italic> mission.</jats:p>