1. Project management Project manager must;
· Plan the Project: Very simply stated, a good plan saves time and reduces the cost of the project. Or, alternatively defined, a bad plan costs time and money, reduces profit and can easily result in a loss and/or bankruptcy.
· Estimate the Cost and Establish the Budget: Budget is a very important factor since it establishes the limits to which costs can be taken. Ultimately cost is the driving factor behind the majority of resources that are needed in a project.
· Identify and Acquire Necessary Resources (People, Equipment, etc.) productive teams can significantly improve project efficiency. Skills that are needed in a project need to be resourced during the planning stages so that costs can be determined.
· Manage the project (to the schedule and within budget): Not everything can be planned. There are always potential problems that cannot be foreseen. Contingency plans need to be in place in order to mitigate the effects of unforeseen problems.

2. Managing a project involves a number of stages
Establish requirements, which will serve to guide all the other stages of the project.
establish a timed relationship between the available resources and the project deliverables
identify problems that are not easy to spot during the planning phase.
Validation: “are we building the correct system”?
Verification: are we building the system in the correct way.
Build it: If a design error is built into the implemented system, it could be very difficult
project is delivered to the client, and measured against the original set of agreed requirements

3. Requirements Engineering
Legal basis: It can serve to establish the basis for agreement between the clients and the suppliers on what the project will provide.
Reduced development effort. A formal requirements document encourages the various concerned parties to consider rigorously all of the requirements before design begins. This helps to reduce effort in subsequent redesign, modifications and retesting. Careful review of the requirements can reveal omissions, misunderstandings, and inconsistencies early in the development cycle when these problems are easier to correct.
Provide a basis for estimating costs and schedules. The description of the product to be developed can be used as a realistic basis for estimating project costs. This in turn helps both the clients and the suppliers because they can both make business decision based on this.
Provide a baseline for validation and verification. Project can be validated much more easily if a good requirement document is in place.

4. Requirements Documentation
User requirements
System requirements
Requirements definition: This is the definition of the aims form the user perspective.
What is the system or project aiming to achieve?
These should be defined to a point where the project can proceed with an acceptable level of risk.
Requirements definition: This is the definition of the aims form the system perspective.
These should also consider resource implications on system development. (i.e. have we done something like this before?)
Requirements specification: Effectively these are the objectives that need to be met in order that the aims can be satisfied. This will normally consist of functional and Non-Functional requirements
Requirements specification: Objectives as outlined in the user requirements, but from the systems perspective.
It should be clear that some objectives would be different when looking at the system as opposed to the user requirements.

5. Functional requirements: As the name implies, these refer to functions provided by the system for the user.
Therefore these requirements are statements that describe how the user and the system are expected to react to particular inputs. In other words functional requirements specify particular behaviours of a user and or a system, or the interaction between these.
Non-functional requirements: These relate to the quality and attempt to quantify the value added components of a system and a user.
Generally these will relate to the functional requirements since they operate in the same environment.
For, example, if the system is a manufacturing process, and the user is a process operator, then non-functional issues could be the timing performance on the services or functions offered by the system.
On the other hand, if a project were to design a new architecture for a game console, which is based on RISC technology, then the non-functional requirements would include constraints on the development process, standards, etc.
Typical non-functional requirements include, reliability, scalability, and cost

6. Planning issues
Cost: A cost estimate establishes the base line of the project cost at different stages of the project.
In science and engineering projects we can use formulas

7. Three Types of Models are identified

8. Modelling
Iconic models: These use a physical representation of a real object, such as for example, a scale model of a formula 1 car.
Analogue models: These are also physical in form, but rather than represent the physical dimensions, these models describe the meaning and they can be used too represent dynamic situations statically. For example, state transition models are used to depict how a system traverses between states after an event occurs. A system flowchart is another example of this type of model as is a data flow diagram or an entity relationship (ER) diagram in database work.
Mathematical models: These models use symbols and mathematical relationships to represent reality. Being mathematical, these can be manipulated in ways that the actual problem components cannot. For example, if a mathematical model of a flying machine demonstrates that it will crash, no one gets hurt because it will not be built in that way. Studying and analysing the mathematical model can draw conclusions regarding the real problem.

9. Mathematical model structure
Optimisation Tools:Linear programming (LP) involves the use of mathematical techniques to obtain an optimum solution in resource allocation problems, such as for example in production planning. Mathematically speaking, by suitable differentiation, it is possible to obtain the maximum and minimum values of any continuous function involving two variables. If the function involves more than two variables, then partial differentiation can be used.