You'll need to find that out directly from the printer. Most will be able to use, and will prefer, the EPS you have been given in the package provided. The lower resolution JPGs provided are for use in web applications. Theyt cannot be used by your printer for any practical purpose.
In most cases, the printer will be able to use the EPS to create all the product you'll need.
Some products require higher resolution JPG or other types of files. This type of file is not provided with the package you receive.
Web Designers may ask for a layered PSD (Photoshop) file in high resolution. This type of file is not provided with the package you receive - please contact the winning Designer and have the files created for you.