Tally of total expected per week of the year

Hi, I need help - I need to predict how many interviews are upcoming each week for the rest of the year. I have already created a sheet with all the projects the timelines for data collection and then a column with the average interview expected per week (within each project). Now I wanted to add up that expected average and project a total of expected interviews for the rest of the week. I think a SUMIFS function can facilitate this but do not know if conditioning for date ranges is possible. See below for what I am expecting to extract. THANKS.

NOTE: the original sheet I am trying to link from includes columns with the following information: project specific start and end dates, total of interviewes, total duration (in weeks), and interviews/week expected.

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