Date calculation based on data in a spreadsheet to identify start date for material

I have a spreadsheet that has a row range showing inventory depletion. The headers to these rows have a date. I also have a cell with a number in that represents how many days it takes to manufacture a lot of material. I need to identify when inventory turns negative in the first range, then look at the date in the header of that column, then calculate the start date going backwards from that date based on the number in the cell I have identified is the manufacturing time. No idea how to write this?