Draw a class diagram, showing the relevant classes, attributes, operations, and relationships for each of the following situations (if you believe that you need to make additional assumptions, clearly state them for each situation):
a. A company has a number of employees. The attributes of Employee include employeeID (primary key), name, address, and birth date. The company also has several projects. Attributes of Project include projectName and startDate. Each employee may be assigned to one or more projects, or may not be assigned to a project. A project must have at least one employee assigned, and it may have any number of employees assigned. An employee’s billing rate may vary by project, and the company wishes to record the applicable billing rate for each employee when assigned to a particular project. At the end of each month, the company mails a check to each employee who has worked on a project during that month. The check amount is based on the billing rate and the hours logged for each project assigned to the employee.

b. A university has a large number of courses in its catalog. Attributes of Course include courseNumber (primary key), courseName, and units. Each course may have one or more different courses as prerequisites, or a course may have no prerequisites. Similarly, a particular course may be a prerequisite for any number of courses, or it may not be a prerequisite for any other course. The university adds or drops a prerequisite for a course only when the director for the course makes a formal request to that effect.

c. A laboratory has several chemists who work on one or more projects. Chemists also may use certain kinds of equipment on each project. Attributes of Chemist include name and phoneNo. Attributes of Project include projectName and startDate. Attributes of Equipment include serialNo and cost. The organization wishes to record assignDate—that is, the date when a given equipment item was assigned to a particular chemist working on a  pecified project—as well as total Hours, that is, the total number of hours the chemist has used the equipment for the project. The organization also wants to track the usage of each type of equipment by a chemist. It does so by computing the average number of hours the chemist has used that equipment on all assigned projects. A chemist must be assigned to at least one project and one equipment item. A given equipment item need not be assigned, and a given project need not be assigned either a chemist or an equipment item.

d. A college course may have one or more scheduled sections, or it may not have a scheduled section. Attributes of Course include courseID, courseName, and units. Attributes of Section include sectionNumber and semester. The value of sectionNumber is an integer (such as 1 or 2) that distinguishes one section from another for the same course, but does not uniquely identify a section. There is an operation called findNumSections that finds the number of sections offered for a given course in a given semester.

e. A hospital has a large number of registered physicians. Attributes of Physician include physicianID (primary key) and specialty. Patients are admitted to the hospital by physicians. Attributes of Patient include patientID (primary key) and patientName. 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 he or she may not treat any patients. Whenever a patient is treated by a physician, the hospital wishes to record the details of the treatment by including the date, time, and results of the treatment.