Final answer:
Accurate duration and cost estimates are best determined after the requirements gathering phase of the engineering design process, where detailed planning and understanding of the project are developed. Mathematical models are used to estimate costs based on the science and implementation details, which are then refined through prototyping, testing, and refinement stages.
Step-by-step explanation:
Accurate duration and cost estimates can be determined after the requirements gathering phase. This stage of the engineering design process is crucial, as it involves detailed planning and an in-depth understanding of the project's needs and constraints. By the end of the requirements workflow, the team will have gathered enough information to make informed estimations about time and resources needed to complete the project.
Mathematical models play a key role in estimating costs and can help analyze the relationship between the science behind a technique and its implementation cost. These models take into consideration various factors such as materials, fabrication, manufacturing, operation, and maintenance costs. Once the project reaches the detailed design phase, the team will have refined their understanding of these costs even further, allowing for more precise estimates that will guide the development process and ensure the project stays on budget.
While initial estimates may be made during the initial planning phase, they are often rough and subject to change as more information becomes available and the project progresses through subsequent stages like prototyping, testing, and refinement. These activities provide valuable feedback that can significantly influence the project's budget for product development and its design direction, ultimately contributing to the success or failure of the final product.