So, raising the price on TP does nothing to increase supply in a 1 month time frame and reduces availability to the poorest. Instead, reduce demand with a bidet and limit customer purchases.
If you have some plants that are not at capacity, you can hire additional shifts to produce more, run on weekends, etc. Then you have additional labor costs, overtime, materials costs, etc. to recoup.
The manufacturing plant I once worked for had spare capacity for the better part of a decade, so it's not some completely unusual thing and was in fact part of our corporate strategy at the time to gain market share.
A new shift will take a while to train up and temps are... ugh... don't even get me started about the sort of people temp agencies send. We had some that only lasted a day for not listening and doing stupidly unsafe things. One of them nearly hit me upside the head with a piece of glass because he wasn't paying attention to where he was swinging it. That was his last day on the job, for precisely that reason.
What is the ideal pricing to achieve long term goals wasn't something I was addressing.
If anything it's the opposite.
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.
If home toilet paper demand will only be high for 2 years you can't make money.
You also want prices to increase to discourage hoarding. Otherwise what happens is that people with disposable income just strip the shelves because there is no possible downside to hoarding toilet paper. They can just not buy it later with no loss to themselves if the price is the same.