$2.$ The following data structure and constraints exist for a magazine publishing company:

a$.$ The company publishes one regional magazine in each of four states: Florida $($FL$),$ South Carolina $($SC$),$ Georgia $($GA$),$ and Tennessee $($TN$).$

b$.$ The company has $300,000$ customers $($subscribers$)$ distributed throughout the four states listed in Problem $2$a$.$

c$.$ On the first day of each month, an annual subscription INVOICE is printed and sent to each customer whose subscription is due for renewal. The INVOICE entity contains a REGION attribute to indicate the customer's state of residence $($FL$,$ SC$,$ GA$,$ TN$)$:

CUSTOMER $($CUS$\_$NUM, CUS$\_$NAME, CUS$\_$ADDRESS, CUS$\_$CITY, CUS$\_$ ZIP, CUS$\_$SUBSDATE$)$

INVOICE $($INV$\_$NUM, INV$\_$REGION, CUS$\_$NUM, INV$\_$DATE, INV$\_$TOTAL$)$

The company is aware of the problems associated with centralized management and has decided to decentralize management of the subscriptions into the company's four regional subsidiaries. Each subscription site will handle its own customer and invase data. The management at company headquarters, however, will have access to customer and invoice data to generate annual reports and to issue ad hoc queries such as:

$$ Listing all current customers by region

$$ Listing all new customers by region

$$ Reporting all invoices by customer and by region

Given these requirements, how must you partition the database?

$3.$ Given the scenario and requirements in Problem $2,$ answer the following questions:

a$.$ What recommendations will you make regarding the type and characteristics of the required database system?

b$.$ What type of data fragmentation is needed for each table?

c$.$ What criteria must be used to partition each database?

d$.$ Design the database fragments. Show an example with node names, location, fragment names, attribute names, and demonstration data.

e$.$ What type of distributed database operations must be supported at each remote site?

f$.$ What type of distributed database operations must be supported at the headquarters site?