Hoping someone can help me!

I am looking for a formula that will sum a range based on a vertical criteria and a horizontal criteria - but this second one is actually a date range not a single date.

I have dates in row 1 and variables in column A (see linked image below).

I am looking for a formula that will sum multiple cells based on a start and finish date for a certain 'variable'.

For example - In the linked image I have 3 fields that are input (the yellow cells C11, C12 & C13). Using these 3 fields I want it to find the cells they are referring too (the blue cells) and give the sum of these in the "total" (green cell F11)

Can anyone help with a formula?