Efficient way to concatenate row titles based on column indicator?

Question

I have a list of ingredients in column A, and different products in columns. The products all consists of different combinations of the same ingredients. In each product's column, there are Y indicators for inclusion of that row's ingredient.

Is there a more efficient way to concatenate the list of ingredients for each product (shown in row 14 in my example)? In my example, I manually check each row for a "Y," then add that ingredient to the string. In my real-life project, I've got over 100 "ingredients" spread across 85 "products." Can I accomplish this same result with some kind of array formula, or do I have to resort to a VBA coded loop?