Adding cells containing/related to certain text

In the spreadsheet attached, I'm trying to get a total of all the specific types of systems shipped throughout a year. These totals should go in the red-background boxes at the top. For instance, the total for System AAA should be 3. The total for System BBB should be 6, etc.

I'm not sure how to tell Excel to add up the numbers from all the different customers only pertaining to the AAA Type of System. Could someone explain how to do so, and perhaps give me a function that will perform my desired action?

Thanks!