There are two ways to add a new producer:
From the Producers tab
Click on the Producer tab
On the left-hand side, click Add Producer
Optionally assign an importer to a producer
When a new Product is created with this Producer and an Importer is specified here, then that Product will also be made with this Importer
By creating a new product
Click on the Products tab
On the left click on New Product
On the next page, you can enter your new Producer name in the field
Continue to create your new product. Upon save, the Producer will be created