my $pr1 = qq{select customer_name  from customer  where id = $emp_id }
+;

my $sth1 = $dbh->prepare($pr1);
$sth1->execute();
$cust_id;
$sth1->bind_columns( undef, \$cust_id );
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I reckon that inspite of the name of the variable it actually contains customer_name which you are comparing with $emp_id which is probably not what you want.

Notes: Use strict and warnings
You most likely could do this with a JOIN. Check the SQL docs.

Update: Also, have a look at Placeholders in the mighty DBI docs.