Min If with a Twist

Hi guys,

I am looking to summarize a report's findings, and I would like to do so with a formula rather than updating it manually each month. I have a list full of multiple categories, and each category contains several locations. This is what I would like the formula to do: Look for the minimum value of savings within the same location, then return the category in which this minimum falls into. Right now, I am using a {=min(if function which correctly returns the minimum savings for each location, but I would like it to return the category name for which the minimum savings falls under.

This description of my problem is pretty confusing I bet so I will attach a sample spreadsheet. Please note that there are two small tabs. My actual spreadsheet of course has many more categories than this.

Thanks,

David