How are constitutive enzymes regulated?
A constitutive or "housekeeping" enzyme is usually defined as an enzyme whose expression level (amount of protein) is always constant, independent of any environmental factors. Hence, regulation of constitutive enzymes must be post-translational, for example allosteric regulation of the enzymatic activity by substrates or products.

Note that constitutive enzymes is mostly a theoretical concept. There are probably no enzymes whose expression is completely unaffected by any environmental factor.