Backgrounding Shed

Hello all,
I am considering building a shed for backgrounding calves and wanted to get opinions from experts.
My plan was to build a 30x50 shed possibly with a concrete floor to keep some calves in.
I figured I could buy some 3-400lb calves at the auction put 2-300lbs on them and send them back to the sale. I know it's probably not the most profitable system but I could get rid of some hay that isn't horse quality. I was planning on giving them free choice hay and feeding ground ear corn/soybeans mix around 14% protein.

My main question was how many calves would a 30x50 barn support? They'll have access to an acre lot around the barn and I'd like to have several calves but I also don't want a muddy nasty mess because I have too many.

I hope you'll all weigh in on this and any tips would be appreciated. I've had more experience in row croos than livestock even though I've been around cows my whole life.

Backgrounding Shed