Lookup value in table if header date falls within this range

[B5rocksass]

I need to compile a list of item qtys across a weekly grid for reporting purposes. My original sheet is a list with duplicates. How do I arrive at the conclusion in the second table using formulas? Right now I'm doing this manually.

[TABLE="width: 521"]
<tbody>[TR]
[TD]ITEM
[/TD]
[TD]QTY SHIPPED
[/TD]
[TD]IN-HOUSE DATE (OR EST)
[/TD]
[TD][/TD]
[TD]WEEK START
[/TD]
[TD="align: right"]1/22/17
[/TD]
[TD="align: right"]1/29/17
[/TD]
[TD="align: right"]2/5/17
[/TD]
[TD="align: right"]2/12/17
[/TD]
[/TR]
[TR]
[TD]DOG
[/TD]
[TD]500
[/TD]
[TD]25-Jan
[/TD]
[TD][/TD]
[TD]DOG
[/TD]
[TD="align: right"]750
[/TD]
[TD="align: right"]350
[/TD]
[TD="align: right"]0
[/TD]
[TD="align: right"]500
[/TD]
[/TR]
[TR]
[TD]HORSE
[/TD]
[TD]250
[/TD]
[TD]25-Jan
[/TD]
[TD][/TD]
[TD]CAT
[/TD]
[TD="align: right"]0
[/TD]
[TD="align: right"]450
[/TD]
[TD="align: right"]0
[/TD]
[TD="align: right"]600
[/TD]
[/TR]
[TR]
[TD]DOG
[/TD]
[TD]250
[/TD]
[TD]25-Jan
[/TD]
[TD][/TD]
[TD]HORSE
[/TD]
[TD="align: right"]1,250
[/TD]
[TD="align: right"]0
[/TD]
[TD="align: right"]0
[/TD]
[TD="align: right"]600
[/TD]
[/TR]
[TR]
[TD]CAT
[/TD]
[TD]500
[/TD]
[TD]25-Jan
[/TD]
[TD][/TD]
[TD]PIG
[/TD]
[TD="align: right"]550
[/TD]
[TD="align: right"]250
[/TD]
[TD="align: right"]0
[/TD]
[TD="align: right"]200
[/TD]
[/TR]
[TR]
[TD]HORSE
[/TD]
[TD]1,000
[/TD]
[TD]25-Jan
[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD]PIG
[/TD]
[TD]550
[/TD]
[TD]25-Jan
[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD]PIG
[/TD]
[TD]250
[/TD]
[TD]2-Feb
[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD]DOG
[/TD]
[TD]350
[/TD]
[TD]2-Feb
[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD]CAT
[/TD]
[TD]450
[/TD]
[TD]2-Feb
[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD]DOG
[/TD]
[TD]500
[/TD]
[TD]16-Feb
[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD]CAT
[/TD]
[TD]600
[/TD]
[TD]16-Feb
[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD]HORSE
[/TD]
[TD]600
[/TD]
[TD]16-Feb
[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD]PIG
[/TD]
[TD]200
[/TD]
[TD]16-Feb
[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
</tbody>[/TABLE]

 

[Momentman]

The cell coloured yellow should be 500, you have it as 0 in your sample

Excel 2010
	A	B	C	D	E	F	G	H	I	J
1	ITEM	QTY SHIPPED	IN-HOUSE DATE (OR EST)		WEEK START	22-Jan	29-Jan-17	05-Feb	12-Feb-17	19-Feb
2	DOG	500	25-Jan		DOG	750	350	0	500
3	HORSE	250	25-Jan		CAT	500	450	0	600
4	DOG	250	25-Jan		HORSE	1250	0	0	600
5	CAT	500	25-Jan		PIG	550	250	0	200
6	HORSE	1,000	25-Jan
7	PIG	550	25-Jan
8	PIG	250	02-Feb
9	DOG	350	02-Feb
10	CAT	450	02-Feb
11	DOG	500	16-Feb
12	CAT	600	16-Feb
13	HORSE	600	16-Feb
14	PIG	200	16-Feb
Sheet6

Cell Formulas
Range	Formula
F2	=SUMIFS($B$2:$B$14,$A$2:$A$14,$E2,$C$2:$C$14,">="&F$1,$C$2:$C$14,"<"&G$1)

 

[B5rocksass]

YOU ARE A GENIUS! Thank you so much!!