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1. **Understand the Problem**  
   Engineers first work to **define the problem clearly**. This involves determining what needs to be solved and why it is important. During this stage, they ask questions like:  
   - What is the intended function of the solution?  
   - What challenges might be encountered?

2. **Identify Criteria and Constraints**  
   Once the problem is understood, engineers determine:  
   - **Criteria:** The attributes of a good solution (e.g., efficiency, safety, cost-effectiveness).  
   - **Constraints:** The limitations placed on the design, such as available materials, time, budget, and environmental factors.  
   These can be expressed generally as:  
   $$
   \text{Design Criteria} \subseteq \text{Overall Requirements}
   $$
   and  
   $$
   \text{Design Constraints} \subseteq \text{Problem Limitations}
   $$

3. **Develop a Plan**  
   Based on the defined problem, criteria, and constraints, engineers create a plan that often includes:  
   - Selecting possible design approaches  
   - Listing required materials and tools  
   - Outlining a workflow for prototyping and testing

4. **Assemble the Prototype**  
   Following the plan, the next step is to **build a prototype**, which is a tangible model of the proposed solution. The prototype serves as a practical means to investigate whether the design meets the necessary criteria.

5. **Test the Prototype**  
   Once the prototype is built, engineers rigorously test it against the established criteria. The tests verify if the prototype meets performance standards and if it complies with the constraints.

6. **Evaluate and Iterate**  
   Finally, the results of the tests help to evaluate whether the solution is effective. If the prototype meets the criteria, it may move forward to final production. Otherwise, the design is refined and the process is repeated with adjustments to better meet the criteria and constraints.
1. **Define the Problem** Engineers start by clearly understanding the problem and its importance. 2. **Set Criteria and Constraints** They determine what a good solution should achieve and the limitations they must work within. 3. **Create a Design Plan** Based on the problem and constraints, they outline the steps needed to develop a solution, including material and tool selection. 4. **Build a Prototype** They construct a model of the proposed solution to test its feasibility. 5. **Test the Prototype** They evaluate the prototype against the set criteria to ensure it meets the required standards. 6. **Refine and Repeat** If the prototype meets the criteria, it's ready for production. If not, they make adjustments and repeat the process.

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