Add Up Numbers In Column Based On Text In Another

I quickly put together an inventory form on our company server where employees can essentially just enter part numbers, quantities, and a few other things, rather than write everything out. So what might happen is, an employee puts together a list of 10 items with their respective quantities, but a few days later, another employee pulls up the spreadsheet and needs to add a few more of a part already listed. Protocol for the company is to do a separate line, rather than add it to the line where the item is already listed. What I am trying to do is, create a separate sheet within that workbook, that simply lists the part numbers, in order, with their total quantity. I have attached a basic spreadsheet showing what I would want, with a tab at the bottom labeled, "What I want."