What do you do if you want to impress employers with your mathematical modeling experience in an interview?

An interview only happens when the employer sees the potential of abilities developed in prior work in the position they are recruiting for. In order to formulate and answer mathematical questions in a new discipline, much knowledge of context is needed, something only possible for those with much experience in the area (ex: logistics). These are typically the constraints of optimization problems, static or dynamic. They can also be the data sets that generate machine learning or neural network models. Hence, it is usually self defeating to show examples in a field you are unfamiliar with. Showing your methods clearly with their assumptions in the context of a problem you are familiar with is beneficial to both interviewer and audience.

I cannot overstate the insignificance of highlighting my contributions "key contributor to two products having quarter billion dollar annual sales". So I also cite good small programs I've written and posted at public internet sites, such as rosettacode.org, quora.com, and the long gone devshed.com.

The valid portion of mathematics is more efficient counting via approximations of various kinds made possible by problem conditions. Communicating in this language makes most material universally accessible so long as the audience is also practical problem solvers performing calculations from physical measurements of various kinds. All practical value for a biological organism including us, arises from either harnessing more energy into the ecosystem or in the modern economy, reducing energy overhead or energy use inefficiency which translates as cost reduction or profit maximization in a business subject to market conditions. Market conditions mean decision makers pay for the consequences of their decisions and cannot shift them to others.

I would lead with this. Talk about a project you have worked on where you aligned the model with the business. Typically, people think that good modeling means primarily writing a model that a solver can solve efficiently. And that is true, but table stakes. Instead, give an example where you realized that the original model was actually not aligned with what creates value in the business. This shows that you are not just technically strong, but can apply your technology in the context of economical objectives.

Talk about an earlier project you have contributed. One may start by saying about the project objective and its impact on business. Also it is worth mentioning about the complexities you have handled through your modeling. People may not know the link between business and modeling. Establishing this connection may give a good mileage. Make a simple dummy model, or you may take a small version of your complex model, or a sandbox model. Solve it in front of them if time permits and explain the features and applicability. The main thing needs to be mentioned that OR modeling does not depend on explicit data unlike ML modelling, rather it depends on formulation.