Advantages Of Linear Programming Model

Aim
To provide an overview of linear programming model and its business applications
Instructional Objectives
After completing this chapter, you should be able to:
• Outline the structure of Linear programming model
• Explain the advantages of Linear Programming
• Express the limitations of Linear programming
• Identify the situations in which linear programming model can be applied
Learning Outcomes
At the end of this chapter, you are expected to:
• Describe the structure of Linear Programming model
• Illustrate the benefits of Linear programming approach
• Comprehend the limitations of Linear Programming approach
• Assess the situations in which linear programming model can be applied

Opening Case-let “Hi Raj, at last, got the approval

Watch the video from the link mentioned below: https://www.youtube.com/watch?v=gfy6xc7iqdE for better understanding of this section 2.1.1
A real situation can be expressed in a linear programming problem form when the following requirements are met.
Requirements are as follows:
• There should be a clear, specific and measurable objective such as maximisation of profit, minimisation of cost and more.
• There should be clearly identifiable, measurable activities (that is decision variables) such as number of units to be produced, number of bags and more
• There should be identifiable and measurable, a limited supply of resources to meet the attainment of the goal.
• All the relationships shown by the objective function and the resource constraints should be linear in nature.
• There should be a set of feasible alternative courses of action available.
S.D Sharma, in his book “Operations Research: Theory and applications” defined linear programming problem as

They are:
i. Decision variables ii. Objective function iii. Constraints

Figure 2.1.1: Elements of Linear programming Model

i. Decision variables
Decision variables are certain activities that have to be done for the certain extent to optimise the objective function. They are denoted by x1, x2, x3 …xn.
For example, in a production case where the objective function is to maximise the profits with the limited resources, the production of a number of units of Product A and Product B represents the decision variables.
If the decision maker can manipulate the values of the variable, then it is known as a controllable variable. In a linear programming model, all the decision variables are controllable, continuous and non-negative. ii. The Objective Function
It is a mathematical representation of a measure of performance (such as profits, costs and more) which has to be optimised (that is, maximised or minimised).
In its general form, it is expressed in a linear form as follows:
Optimise Z = c1x1 + c2x2 + c3x3 + … + cnxn
Where Z is the measure of performance, x1, x2, x3 …xn are the decision