PART II: APPLICATIONS OF LINEAR FUNCTIONS
Chapter 02
The Straight Line and Applications
Chapter overview
This chapter introduces applications of linear function (straight line). The straight line serves as a
model for numerous economic/business situations: demand, supply, cost, revenue, consumption, and
savings.
Topics covered in this chapter:
PART II: The Applications of Linear function (Straight Line)
Demand; Supply; price
Cost functions
Total revenue functions
Profit
PREPARED BY: S. SRITHARAN 1
, PART II: APPLICATIONS OF LINEAR FUNCTIONS
PART II: Applications of Linear Functions (Straight Line)
Learning Outcomes:
At the end of this section you should be able to:
• Understand what the term 'mathematical modelling' means
• Model (i) graphically and (ii) algebraically (writing down their equations) the following basic
functions:
Demand and supply
Cost
Revenue
Profit
2.11 Mathematical Modelling
This section will help you understand mathematical models and how they are used in the context of
business.
What is a Model?
A ‘model’ is a representation of reality.
Different types of models are used to represent reality. For example,
Architectural firms use physical models to help decision-makers determine how a building
may look.
Engineers sometimes build small scale models to make sure that a new plant will operate as
designed.
Software developers use schematic models or pictures, drawings, and charts to describe the
functionality of their products.
Mathematical Model
Mathematics can be used to represent real-world situations. The tools used to represent real world in
such a manner are called mathematical models. Thus, Mathematical model is an abstract
model that describes a real-world problem, environment, or system using a mathematical concepts
and language. Mathematical models are typically in the form of equations or other mathematical
statements. They help to understand how the real world works. Most models don't recreate the real
world as it is, but they offer a simplified approximation of the real-world situations.
Businesses use mathematical models in several ways.
Examples:
The Profit and Loss Model:
Profits are the amount by which revenues exceed expenses, and losses are the amounts by which
expenses exceed revenue. This relationship can be described as a mathematical model by the equation:
PREPARED BY: S. SRITHARAN 2
, PART II: APPLICATIONS OF LINEAR FUNCTIONS
Revenue – Cost = Profit (or Loss if negative)
The above equation or formula called ‘The Profit and Loss Model’ is a tool that businesses use to
describe their profit (or loss).
Using this mathematical model as a basis, the following relationships can be deuced with the laws of
arithmetic:
Revenue = Profit - Cost Cost = Revenue - Profit
Net Present Value Model (NPV Model)
One of the most common decision-making problem faced by any business is the investment decision,
where it must decide whether to invest in a project or not. Businesses often use mathematical models
that assess the potential valuation of the project against the investment to be made for making such
decisions. Examples of such models are net present value (NPV), internal rate of return (IRR), etc. A
simple NPV model can be illustrated as below:
Note:
Every mathematical model requires a set of inputs and mathematical functions to generate an output.
Mathematical Modelling:
Mathematical modelling simply refers to the process of developing mathematical formulas (equations
or inequalities) to represent a real world problem in mathematical terms. Laws of arithmetic and
algebra can be used to develop models, and to solve them.
Steps in Solving Problems Based on Mathematical Models:
In solving problems based on mathematical models, it is helpful to take the following steps:
1) Develop a Model. Choose or invent a model that describes the realities you are facing. For
instance, if you need to determine what profit a business will have this year, the profit and loss
model would be appropriate.
PREPARED BY: S. SRITHARAN 3
Chapter 02
The Straight Line and Applications
Chapter overview
This chapter introduces applications of linear function (straight line). The straight line serves as a
model for numerous economic/business situations: demand, supply, cost, revenue, consumption, and
savings.
Topics covered in this chapter:
PART II: The Applications of Linear function (Straight Line)
Demand; Supply; price
Cost functions
Total revenue functions
Profit
PREPARED BY: S. SRITHARAN 1
, PART II: APPLICATIONS OF LINEAR FUNCTIONS
PART II: Applications of Linear Functions (Straight Line)
Learning Outcomes:
At the end of this section you should be able to:
• Understand what the term 'mathematical modelling' means
• Model (i) graphically and (ii) algebraically (writing down their equations) the following basic
functions:
Demand and supply
Cost
Revenue
Profit
2.11 Mathematical Modelling
This section will help you understand mathematical models and how they are used in the context of
business.
What is a Model?
A ‘model’ is a representation of reality.
Different types of models are used to represent reality. For example,
Architectural firms use physical models to help decision-makers determine how a building
may look.
Engineers sometimes build small scale models to make sure that a new plant will operate as
designed.
Software developers use schematic models or pictures, drawings, and charts to describe the
functionality of their products.
Mathematical Model
Mathematics can be used to represent real-world situations. The tools used to represent real world in
such a manner are called mathematical models. Thus, Mathematical model is an abstract
model that describes a real-world problem, environment, or system using a mathematical concepts
and language. Mathematical models are typically in the form of equations or other mathematical
statements. They help to understand how the real world works. Most models don't recreate the real
world as it is, but they offer a simplified approximation of the real-world situations.
Businesses use mathematical models in several ways.
Examples:
The Profit and Loss Model:
Profits are the amount by which revenues exceed expenses, and losses are the amounts by which
expenses exceed revenue. This relationship can be described as a mathematical model by the equation:
PREPARED BY: S. SRITHARAN 2
, PART II: APPLICATIONS OF LINEAR FUNCTIONS
Revenue – Cost = Profit (or Loss if negative)
The above equation or formula called ‘The Profit and Loss Model’ is a tool that businesses use to
describe their profit (or loss).
Using this mathematical model as a basis, the following relationships can be deuced with the laws of
arithmetic:
Revenue = Profit - Cost Cost = Revenue - Profit
Net Present Value Model (NPV Model)
One of the most common decision-making problem faced by any business is the investment decision,
where it must decide whether to invest in a project or not. Businesses often use mathematical models
that assess the potential valuation of the project against the investment to be made for making such
decisions. Examples of such models are net present value (NPV), internal rate of return (IRR), etc. A
simple NPV model can be illustrated as below:
Note:
Every mathematical model requires a set of inputs and mathematical functions to generate an output.
Mathematical Modelling:
Mathematical modelling simply refers to the process of developing mathematical formulas (equations
or inequalities) to represent a real world problem in mathematical terms. Laws of arithmetic and
algebra can be used to develop models, and to solve them.
Steps in Solving Problems Based on Mathematical Models:
In solving problems based on mathematical models, it is helpful to take the following steps:
1) Develop a Model. Choose or invent a model that describes the realities you are facing. For
instance, if you need to determine what profit a business will have this year, the profit and loss
model would be appropriate.
PREPARED BY: S. SRITHARAN 3
