Not every plant is run at a constant 24x7 three shift schedule. There are plenty of businesses that keep some slack in their manufacturing to respond to changes in demand as part of their corporate strategy, especially if they think there's an opportunity to gain market share.
But in my experience, there's usually some slack. Maybe not enough to pick up all the demand, but there's some. Maybe they have three shifts but don't work weekends or such. Then they can have people pulling lots of overtime.
Raw materials are usually well-stocked in advance. There is a limit on how much demand can spike before there are issues, of course, but some industries may have weeks or months worth of raw materials stocked. This is going to be highly variable by industry, though. Something like raw glass is nothing like stocking chickens for processing.
For TP I'd guess that they can stock a lot of raw materials, though. It's not made from anything that's going to go bad on them, so they probably stock up a lot based on whatever is cheapest.