The optimization of dual-energy computed tomography (DE-CT) is challenged by the lack of a theoretical foundation for image quality. This work reports a cascaded systems analysis model that was used to derive signal and noise propagation in DE-CBCT in prevalent Fourier metrics such as the noise-power spectrum (NPS) and noise-equivalent quanta (NEQ). The model was validated in comparison to measurements of the 3D NPS and NEQ in DE-CBCT images acquired using an experimental imaging bench. Task-based detectability index was derived using DE-NPS and NEQ as an objective function in optimizing DE imaging parameters such as the dose allocation factor (D A) and kVp pair. The resulting dose allocation optimization is in agreement with the practice of assigning more dose to the high-energy image (D A < 0.5), and the model provides a quantitative basis for examining the optimal dose allocation as a function of total dose, kVp pair, the presence of electronics noise, and the imaging task. An example optimization is shown for a breast tumor detection task. Using DE decomposition to cancel fibroglandular tissue (rendering a DE-CBCT image of breast tumor against an adipose tissue background) and assuming a total dose of 15mGy, the optimal kVp pair is identified at [45, 105]kVp with DA=0.46. The model is sufficiently general for applications beyond this example, demonstrating utility in the optimization in a broad range of imaging parameters. The model provides a new, valuable framework for understanding the theoretical limits of DE-CBCT imaging performance and maximizing image quality while minimizing radiation dose.