Sum Overlaping days to a month

Hi,

I'm trying to get the days in a week which overlap months allocated to the correct month.
i.e. week ended 03/08/14 needs to have the relevant quantity allocated 4 days worth to July and 3 days worth to August. This needs to be intutitive so that when the weeks change for the following year, no changes to formula is needed.

Attached is an example.

TIA

Stuart