Table: PRODTABLE
PRODID     ....
----------------
WO13.....
WO1300013
WO13....

Table: PRODBOM
PRODID      ITEMID   QTY
----------------------------
WO13.....
WO1300013   123456   10.12
WO1300013   246802   8.58
WO1300013   345678   2.00
WO1300013   123849   4.00
WO1300013   111111   0.50
WO1300013   222222   1.00

Table: ColorCoding
ITEMID     TAG
--------------------
6764389    #123456
7859869    #234567
1111111    #aa33cc
5647358    #bb44dd
2222222    #dd11aa

PRODID       TAG
-----------------
WO13.....
WO1300013   #aa33cc
WO13....

SELECT
	p.prodid,
	a.tag
FROM
	prodtable p
	OUTER APPLY
	(
		SELECT TOP (1) tag
		FROM ColorCoding c
		INNER JOIN ProdBOM b ON b.itemId = c.ItemId
		WHERE b.prodid = p.prodid
		ORDER BY qty ASC
	) a(tag);

select a.prodid
      ,e.tag
  from prodtable as a
       inner join (select b.prodid
                         ,min(itemid) as itemid
                     from (select prodid
                                 ,min(qty) as qty
                             from prodbom
                            group by prodid
                          ) as b
                          inner join prodbom as c
                                  on c.prodid=b.prodid
                                 and c.qty=b.qty
                  ) as d
               on d.prodid=a.prodid
       left outer join colorcoding as e
                    on e.itemid=d.itemid