SUMIF Multiple values within Column

I'm trying to devise a formula that will pick up a 'values' (quantity sold on each day) within a range; mutliple each 'value' times the retail price; and then sum the total price of each item resulting in total sales for that day.

E.g.

------------------------------------- Quantity Sold
Item ------- Retail Price ------ 12/11/11 ----- 12/10/11 ----- 12/09/11-----
Prod X ----- $5 ---- 1 ----- 0 ----- 1-----
Prod Y ----- $4 ----- 0 ----- 2 ----- 0 -----
Prod Z ----- $3 ----- 0 ----- 0 ---- 3
Prod A ----- $10 ----- 1 ----- 1 ----- 1
Prod B ----- $1 ----- 0 ----- 4 ----- 0
Prod C ----- $2 ----- 1 ----- 1 ----- 1

So for the day 12/11/11, I'm looking for a result of $17 = ($5*1+$10*1+$2*1).
12/10/11 --- $26 ($4*2+$10*2+$1*4+$2*1)

Please help!

Thank you.