Introduction:
Case studies are often used in various fields to analyze real-life situations and make informed decisions. They require in-depth understanding and analysis of the given scenario to come up with appropriate solutions. In this response, we will discuss whether case studies can be solved using only theoretical knowledge or if practical application of mathematical concepts is necessary.

Theoretical Knowledge:
Theoretical knowledge refers to the understanding and application of concepts, principles, and theories without practical experience. It involves studying the subject matter and acquiring knowledge through books, lectures, and research. Theoretical knowledge provides a foundation for understanding concepts and can be useful in analyzing case studies to some extent. It helps in recognizing patterns, identifying potential solutions, and making informed decisions based on existing knowledge.

Practical Application of Mathematical Concepts:
Mathematical concepts play a vital role in solving case studies, especially in fields such as finance, engineering, and economics. Practical application of mathematical concepts involves using mathematical tools, techniques, and formulas to analyze data, make calculations, and derive conclusions. It enables a more quantitative and precise analysis of the case study, providing a deeper understanding of the problem at hand.

Importance of Practical Application:
While theoretical knowledge provides a foundation, practical application of mathematical concepts enhances the problem-solving process in case studies. Here are a few reasons why practical application is crucial:

1. Data Analysis: Case studies often involve analyzing large amounts of data, which requires mathematical techniques such as statistical analysis, regression analysis, and optimization. Practical application helps in organizing and interpreting the data to draw meaningful insights.

2. Quantitative Decision Making: Mathematical concepts enable quantitative decision making by providing tools for risk analysis, cost-benefit analysis, and forecasting. This allows for a more objective evaluation of different alternatives and their potential outcomes.

3. Real-world Constraints: Case studies often involve real-world constraints such as limited resources, time, and budget. Practical application of mathematical concepts helps in optimizing these constraints and finding the most efficient solution.

4. Predictive Modeling: Mathematical models and simulations are often used to predict future outcomes and assess the impact of different variables. Practical application of mathematical concepts allows for the development and validation of such models, improving the accuracy of predictions.

Conclusion:
While theoretical knowledge provides a foundation for understanding concepts, practical application of mathematical concepts is necessary to solve case studies effectively. It enables data analysis, quantitative decision making, consideration of real-world constraints, and predictive modeling. By combining theoretical knowledge with practical application, one can approach case studies with a more comprehensive and informed perspective, leading to better solutions.