I would suggest that you put in a row to total  the products  for each week and
then use Sumif() to derive the totals per month.

Working on just the sample given and assuming it starts from cell A1, put the
numbers 1-12 in A11 to A22 and put this formula  in B11 and copy it down.

=SUMIF($C$2:$K$2,A11,$C$9:$K$9)

In this formula $C$2:$K$2 is the month  numbers in row 2 (C2:K2) - for a year
the endpoint will be around BC2
A11 is the cell containing 1 for month 1
$C$9:$K$9 is the row containing the weekly totals.