$1.$ Suppose a manufacturer produces three high$-$cost$,$ low$-$volume products: P$1,$ P$2,$ and P$3.$ Product P$1$ is assembled with components C$1$ and C$2$; product P$2$ is assembled with components Cl$,$ C$3,$ and C$4$; and product P$3$ is assembled with components C$2$ and C$3.$ Components may be purchased from several vendors, as shown in the following table.

$2)$ Suppose a manufacturer produces three high$-$cost$,$ low$-$volume products: P$1,$ P$2,$ and P$3.$ Product P$1$ is assembled with components C$1$ and C$2$; product P$2$ is assembled with components Cl$,$ C$3,$ and C$4$; and product P$3$ is assembled with components C$2$ and C$3.$ Components may be purchased from several vendors, as shown below.

Vendor Component Supplied

V$1$ C$1,$ C$2$

V$2$ C$1,$C$2,$C$3,$C$4$

V$3$ C$1,$C$2,$C$4$

Each product has a unique serial number, as does each component. To track product performance, careful records are kept to ensure that each product$$s components can be traced to the component supplier.

Products are sold directly to final customers; that is$,$ no wholesale operations are permitted. The sales records include the customer identification and the product serial number. Using the preceding information, do the following:

a$.$ Write the business rules governing the production and sale of the products.

b$.$ Create an ER diagram capable of supporting the manufacturer$$s product$/$component tracking requirements.