I am trying to define the last row of column A as a constant, which I am able
to do. Then I want to apply that constant to the MAX and MIN functions, as
so:

Dim LastRow As Long
LastRow = Cells(Rows.Count, "A").End(xlUp).Row
Range("AM4").Select
ActiveCell.FormulaR1C1 = "=MIN(R[7]C:R[LastRow]C)"

But this gives me an error stating Run-Time error '1004':
Application-defined or object-defined error.

I've had success using the LastRow value in the autofill (from other hints
on these boards) as so:

Selection.AutoFill Destination:=Range("BI11:BI" & LastRow)