When to begin eviction process

[Matthew Tanis]

I recently purchased a duplex with 1 long term tenant, 1 shorter term.  It's in a recovering area and rents are reasonable.  Our short term tenant had a third party paying their rent before, but this is the first month they are on their own for rent.  They are late and now past the grace period allotted by the lease.  In Michigan, they need to be given a 'Notice to Quit' good for 7 days before proceeding with a court order.  How long is a reasonable amount of time before beginning the eviction process?