Exercise $5\mathrm{.}5.$ Consider the university data warehouse described in Ex$.3\mathrm{.}3$ Draw a constellation schema for the data warehouse taking into account the different granularities of the time dimension. Exercise $3\mathrm{.}3.$ Consider the data warehouse of a university that contains information about teaching and research activities. On the one hand, the information about teaching activities is related to dimensions department, professor, course, and time, the latter at a granularity of academic semester. Measures for teaching activities are number of hours and number of credits. On the other hand, the information about research activities is related to dimensions professor, funding agency, project, and time, the latter twice for the start date and the end date, both at a granularity of day. In this case, professors are related to the department to which they are affiliated. Measures for research activities are the number of person months and amount. Define the OLAP operations to be performed in order to answer the fol$-$ lowing queries. For this, propose the necessary dimension hierarchies. a$.$ By department, total number of teaching hours during the academic year $2012-2013.$ b$.$ By department, total amount of research projects during the calendar year $2012.$ c$.$ By department, total number of professors involved in research projects during the calendar year $2012.$ d$.$ By professor, total number of courses delivered during the academic year $2012-2013.$ e$.$ By department and funding agency, total number of projects started in $2012.$