How to return merged column header based on match in column A and minimum value in row that

I have a table listing prices broken down by unit cost and retailer.

Item	$	Size	$/oz or Unit	$	Size	$/oz or Unit	$	Size	$/oz or Unit
all purpose flour	$8.00	10	$0.80	$15.00	9	$1.67	$8.00	5	$1.60
apples	$7.00	3	$2.33	$11.00	5	$2.20	$10.00	9	$1.11
applesauce	$5.00	9	$0.56	$13.00	5	$2.60	$6.00	3	$2.00
bacon	$4.00	3	$1.33	$5.00	2	$2.50	$5.00	7	$0.71
bagels	$15.00	3	$5.00	$12.00	6	$2.00	$3.00	6	$0.50
bell pepper	$7.00	3	$2.33	$13.00	2	$6.50	$5.00	4	$1.25

Retailer is a merged cell spanning $, Size, and $/oz or Unit. $/oz or unit is an arrayformula dividing the previous 2 columns.

I am trying to get the minimum cost per unit and return the retailer, size, and cost on a second sheet.

I've tried using query's and index match functions, but I cannot wrap my head around how to query against multiple criteria.

This is a copy of the sheet to clarify. https://docs.google.com/spreadsheets/d/1mRYX7r-ExODhs57GOpctGXLxSmNf5UEJwWw0KJmb6eU/edit?usp=sharing

Solution

You may try:

=let(common_,Stores!A3:A, group_,Stores!B3:S, header_,Stores!B1:S1, size_,3,
     Σ,reduce(,sequence(columns(group_)/size_,1,1,size_),lambda(a,c,vstack(a,{common_,let(Λ,choosecols(header_,c),wrapcols(Λ,rows(group_),Λ)),choosecols(group_,sequence(size_,1,c))}))),
     〱,sort(filter(Σ,index(Σ,,1)<>""),5,1), map(A2:A,lambda(丨,if(丨="",,index(ifna(vlookup(丨,〱,{2,3,4,5},)))))))

Clear the column E Grocery List_tab of any existing formula(s) prior to applying the formula in Cell_B2 so as for the formula to expand freely