What is the recipe for cleaning soap scum and caked on dirt in the tub

try 1 cup peroxide with a few drops of dawn dish soap, an old pot scrub brush the one with a handle scrub good and rinse with shower head of not sponge and clean water.

Have you tried a Magic Eraser? or Dobie pad?

Ajax cleanser. Scrub brush or a scrub pad. Elbow grease.

Equal parts of white vinegar and original blue dawn heated in a measuring cup then pour it into a clean spray bottle, spray well let sit 20 to 30 minutes run a magic eraser over the tub then rinse really well , if you do this once a week or so you won't need to use the eraser everything will rinse off, it is great no harsh chemicals and you can get bottle, dawn and vinegar at the dollar store

I just spray straight vinegar. Give that a try.

if its really bad, go hard core to get it on the good side, then use no harsh chemicals to maintain. ( Dollar store. Get a spray bottle of Awesome, it has directions on dilution, awesome ratio to water and can be used on a ton of things, including laundry)

Magic erasers, or CLR