Please create a sample Tableau Packaged Workbook and upload so we can replicate.
Attached the Sample twbx file.
Due to data security, calculations are replaced with zero's.
Thanks for providing the sample. Based on what I'm looking at, you won't be able to produce the PDF in the way you're hoping - this is a pretty specific scenario you're trying to create here and I don't think it's really Tableau's strong suit.
A 'limitation' of Tableau is that it will print the PDF based exactly on what's being shown on the dashboard, there isn't really a way around that. As a result, you would need to find a way to hide your sheets based on user input. So perhaps you could create a parent parameter which is "How many products do you want to see?" which could hide the extra / unneeded sheets, but I'm not even sure that is possible.