Hello Elliot,
Thank you for reaching out, and for using W3 Total Cache Pro.
You only need one license. Once you configure the plugin on the dev environment remove the license key from Performance>General settings, Licensing sub-box, license field and save all settings in the dev website. Re-enter the license in production, verify the license with the “verify license button” and save all settings.
W3 Total Cache Pro should be active after these steps!
Thanks!