Draw the E/R diagrams for the following business rules using Gliffy. Identify all entities, attributes, relationships, primary keys, cardinalities and constraints where appropriate. Each complete entity (including all attributes and primary key) receives one point and each relationship (labeled with cardinalities in both directions) receive one point. Any constraint used correctly, receives two points. 

1. A laboratory has several chemists who work on one or more projects. Chemists may also use certain kinds of equipment on each project. Data tracked for the chemist includes employee ID, name, phone. Equipment attributes include a serial number and cost. Project information is tracked for a project ID and start date. When a piece of equipment is assigned to a chemist working on a specific project, the assignment date is recorded. A chemist must be assigned to at least one project and one equipment item. A given piece of equipment need not be assigned and a given project need not be assigned either a chemist or an equipment item.

2. A hospital has a large number of registered physicians which includes a physician ID and speciality. Patients are admitted to the hospital by physicians. The hospital tracks the patient ID, and name. Any patient who is admitted must have exactly one admitting physician. A physician may optionally admit any number of patients. Once admitted, a given patient must be treated by at least one physician. A particular physician may treat any number of patients, or may not treat any patients. Whenever a patient is treated by a physician, the hospital records the details of the treatment. Components of treatment detail include date, time, and results.

3. An art museum owns a large volume of works of art. Each work of art is described by an item code, title, type, and size; size is further composed of height, width, and weight. A work of art is developed by an artist, but the artist for some works is unknown. An artist ID, name, date of birth, and date of death (which is null for living artists) is recorded for each artist. Only data about artists for works currently owned by the museum are kept in the database. At any point in time, the status of a work of art is either on display at the museum, held in storage, away from the museum as part of a traveling show, or on loan to another gallery. If on display at the museum, the art's location within the museum is recorded. If the art work is in storage, storage date and return date from storage are recorded. A traveling show is described by a show ID, the city in which the show is currently appearing, and the start and end dates of the show. Many of the museum works may be part of a given show, and only active shows with at least one museum work of art need be represented in the database. Finally, the museum wants to retain a complete history of loaning a work of art to other galleries; a gallery ID, name, and city are recorded for other galleries. Each time a work of art is loaned, the museum wants to record the date the work was loaned and the date it was returned.

4. A technology company provides offerings to its customers. Offerings are of two types; products and services. Offerings are identified by an ID and description. In addition, products are described by product name, standard price, and date of first release; services are described by name of the company's unit responsible for the service and conditions of the service. There are repair, maintenance, and other types of services. A repair service has a cost and is the repair of some product; a maintenance service has an hourly rate.

Fortunately, some products never require repair. However, there are many potential repair services for a product. A customer may purchase an offering, and the company needs to keep track of when the offering was purchased and the contact person for that offering with the customer. Unfortunately, not all offerings are purchased. Customers are identified by an ID, name, address, and phone. When a service is performed, that service is billed to a customer. Because some customers purchase offerings for their clients, a customer may be billed for services he or she did not purchase, as well as for ones that were purchased. When a customer is billed for a service (although some may never require a service of any type), the company needs to keep track of the date the service was performed, the date the bill is due, and the amount due.

5. PROJECTS INC., is an engineering firm with approximately 500 employees. A database is required to keep track of all employees, their skills, projects assigned and departments worked in. Every employee has a unique number assigned by the firm, required to store his
or her name and date-of-birth. If an employee is currently married to another employee of Projects, Inc., the date of marriage and who is married to whom must be stored; however, no record of marriage is required if an employee's spouse is not also an employee. Each
employee is given a job title (for example, engineer, admin assistant, foreman, and so on).

We are interested in collecting more data specific to engineers and admin assistants. The relevant data to be recorded for engineers is the type of degree (e.g., electrical, mechanical, civil, etc.); for admin assistants, it is their typing speed.

An employee does only one type of job at any given time, and we only need to retain information for an employee's current job. There are 11 different departments, each with a unique name. An employee can report to only one department. Each department has a phone number.

To procure various kinds of equipment, each department deals with many vendors. A vendor typically supplies equipment to many departments. We are required to store the name and address of each vendor.

Many employees can work on a project. An employee can work in many projects (for example, Southwest Refinery, California Petrochemicals, and so on) but can only be assigned to at most one project in a given city. For each city, we are interested in its state and population. An employee can have many skills (preparing material requisitions, checking drawings, and so on), but (s)he may use only a given set of skills on a particular project. (For example, employee MURHPY may prepare requisitions for Southwest Refinery project and prepare requisitions as well as check drawings for California Petrochemicals.) Employees use each skill that they possess in at least one project. Each skill is assigned a number, and we must store a short description of each skill. Projects are distinguished by project numbers, and we must store the estimated cost of each project.