I see two options...

1) the cell (e.g. A1) must contain either MINIMUM or MAXIMUM (no blanks or other values) use this formula:

=IF(A1="MINIMUM",IF(C1>=B1,"YES","NO"),IF(C1<=B1,"YES","NO")) --or this formula:
=IF(OR(AND(A1="MINIMUM",C1>=B1),AND(A1="MAXIMUM",C1<=B1)),"yes","no")

2) the cell (e.g. A1) may be blank or contain something other than Min. or Max.

=IF(A1="MINIMUM",IF(C1>=B1,"YES","NO"),IF(A1="MAXIMUM",IF(C1<=B1,"YES","NO"),"N/A")) --or this formula:
=IF(OR(AND(A1="minimum",C1>=B1),AND(A1="maximum",C1<=B1)),"yes",IF(OR(A1="MINIMUM",A1="MAXIMUM"),"NO","N/A"))

Is this what you were looking for?

Bruce