A little known (because it isn't true) fact :- Minister of Productivity, Energy and Industry was the role played by Sid James in the lesser known "Carry On" film "Carry On Forward Not Back", which featured the hilarious antics of Kenneth Williams as the Prime Minister representing the implausibly named "New Labour" party. His catch phrase "I've got the energy if you've got the industry" was much repeated in school playgrounds of the time.
If we are playing slice and dice on ministerial responsibilities, how about the Department of Health, Culture and Productivity or DHCP for short?
Or maybe with a slight renaming, the department of Health and Efficiency? I can imagine the tastefully airbrushed pictures of Tony and Cherie cavorting naked with large beach-balls now.
I think I need to go and lie down in a darkened room.