Consider the following relational schema as part of a university database prof(sin, pname, o_ce, age, sex, specialty, dept did) dept(did, dname, budget, num majors, chair sin) assume the following queries are the most common queries in the workload for this university and they are almost equivalent in frequency and importance assume that both b+ trees and hashed indexes are supported by the dbms and that both single and multiple-attribute index search keys are permitted. specify the attributes you recommend indexing on, indicating whether each index should be clustered or unclustered and whether it should be a b+ tree or a hashed index. note: if you can search with an index-only plan you should create a composite search key 1. find the maximum age of professors in each department. find the name of professors who have a user-specified research specialty list names of the departments with the budget more than 100k. list the department id and chairperson for departments with a user-specified department 2. 3. 4. ame