Cargo containers constitute the most critical component of global trade: 108 million containers represent the movement of about 95% of the world's manufactured goods. The steady increase in cargo container shipments has had a profound effect on world security: the threat associated with smuggling of shielded special nuclear material is elevated every year. Containers reaching the borders of the U.S. are currently not radiographically inspected due to time and dose considerations stemming from the use of bremsstrahlung beams for imaging. Bremsstrahlung spectra are low-energy peaked, resulting in low penetration values, especially through dense cargoes. The use of monoenergetic radiography beams could alleviate many of these problems due to higher energy and low background continuum. Using Monte Carlo simulations of a realistic imaging scenario with support from previous experimental measurements, we demonstrate how the use of monoenergetic photon beams in radiography can simultaneously reduce the radiation dose imparted to the cargo and any potential stowaways while increasing image quality. Dual-energy methods are leveraged to calculate material atomic number. Image quality is evaluated by measuring the noise standard deviation, contrast-to-noise ratio, and the pixel error as the dose is decreased.