Chomp them down

You are a in a burger eating competition. You have a long line of burgers that you need to eat. To eat Burger i you need Mi minutes, and the deadline for eating this burger is Di. You need not eat a burger at a stretch. You can eat a part of it, switch to another burger, and then switch back. You've realized that it might not be possible to eat all the burgers by their deadline. So you decide to