Suppose that a data warehouse consists of three dimensions: time, doctor, and patient, and the two measures count and charge, where charge is the fee that a doctor charges a patient for a visit.

$($a$)$ Enumerate two classes of schemas popularly used for modelling data warehouses.

$($b$)$ Draw a schema diagram for the above data warehouse using one of the schema classes listed in $($a$).$

$($c$)$ Starting with the base cuboid $[$day$,$ doctor, patient$),$ what specific OLAP operations should be performed to list the total fee collected by each doctor in $2004?$

$($d$)$ To obtain the same list, write an SQL query assuming the data are stored in a relational database with the schema fee $($day$,$ month, year, doctor, hospital, patient, count, charge$).$