Finding lowest in column after matching data in another column

Hello, I've been playing around with INDEX and MATCH and MIN and I can't seem to get the formula correct. I'm messing up some logic related to "Only search Costs where Item Name Matches _______".

Here's what I'm trying to do:

Column 1 = Vendor Names
Column 2 = Item Names
Column 3 = Cost of item

I want to match the text in a cell located outside the 3 columns mentioned above with the corresponding text in Column 2, then analyze Column 3 for the lowest cost cell but only in the same rows that the text matches from Column 2, then bring in the Vendor Name from Column 1 from the matched row.

To make this a bit more real, imagine "Cheese" is in a column outside of the above 3 columns. And I have "Cheese" listed in multiple places in Column 2. I'm searching for the vendor with the lowest cost "Cheese".

Perhaps not the best title. Glad to provide more info. Thanks for reading.

Try this ...

=INDEX(A2:A1000,MATCH(MIN(IF(B2:B1000=F2,C2:C1000)),IF(B2:B1000=F2,C2:C1000),0))

Enter with Ctrl+Shift+Enter.

Thank you. Perfect. I really appreciate that!