Using the database city with documents found in the inspections collection, perform the tasks listed below.

a. Update all the documents with the zip code "11242" with the key-value pair "state":"NY" in the address subdocument.

b. Remove the first document with the key-value pair "result":"Violation Issued."

c. Create an index on the key business_name. Show an example query that will use this index with the explain function.

d. Create a compound index that will improve the performance of queries looking for business names that have a Violation Issued in the Retail sector.

e. Create an index that will improve the performance of finding a business by the city location.