Linear Programming:
Let us learn about what we mean by the term Linear Programming,and let us also explore the standard forms of Linear Programming.
Linear Programming is the most popular and widely accepted technique of mathematical programming. The aim of linear programming is to utilize the scarce resources such as man power, man, energy, material and so on. A linear programming problem is one that seeks to maximize or minimize an objective function subjects to constraints. The problem is referred to as linear programming if both the objective function and constraints are linear.
Linear programming (LP) is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear equations.
Structure of Linear Programming Model:
1. Identification of decision variable
2. Define the decision variable
3. Define the objective function
4. Illustrate the constraints to which the objective function should be optimized.
5. Add the non-negative constraints from the consideration
Let us now learn about the standard form of Linear Programming:
Standard form is the usual and most intuitive form of describing a linear programming problem. It consists of the following three parts:
* A linear function to be maximized
e.g., Maximize: c1x1 + c2x2
* Problem constraints of the following form
e.g.,
a1,1x1 + a1,2x2 ≤ b1
a2,1x1 + a2,2x2 ≤ b2
a3,1x1 + a3,2x2 ≤ b3
* Non-negative variables
e.g.,
x1 ≥ 0
x2 ≥ 0.
* Non-negative right hand side constants
bi ≥ 0
The problem is usually expressed in matrix form, and then becomes:
Maximize: cTx
Subject to: Ax ≤ b, x ≥ 0.
Other forms, such as minimization problems, problems with constraints on alternative forms, as well as problems involving negative variables can always be rewritten into an equivalent problem in standard form.
Hope you like the above example of Linear Programming.Please leave your comments, if you have any doubts.
Let us learn about what we mean by the term Linear Programming,and let us also explore the standard forms of Linear Programming.
Linear Programming is the most popular and widely accepted technique of mathematical programming. The aim of linear programming is to utilize the scarce resources such as man power, man, energy, material and so on. A linear programming problem is one that seeks to maximize or minimize an objective function subjects to constraints. The problem is referred to as linear programming if both the objective function and constraints are linear.
Linear programming (LP) is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear equations.
Structure of Linear Programming Model:
1. Identification of decision variable
2. Define the decision variable
3. Define the objective function
4. Illustrate the constraints to which the objective function should be optimized.
5. Add the non-negative constraints from the consideration
Let us now learn about the standard form of Linear Programming:
Standard form is the usual and most intuitive form of describing a linear programming problem. It consists of the following three parts:
* A linear function to be maximized
e.g., Maximize: c1x1 + c2x2
* Problem constraints of the following form
e.g.,
a1,1x1 + a1,2x2 ≤ b1
a2,1x1 + a2,2x2 ≤ b2
a3,1x1 + a3,2x2 ≤ b3
* Non-negative variables
e.g.,
x1 ≥ 0
x2 ≥ 0.
* Non-negative right hand side constants
bi ≥ 0
The problem is usually expressed in matrix form, and then becomes:
Maximize: cTx
Subject to: Ax ≤ b, x ≥ 0.
Other forms, such as minimization problems, problems with constraints on alternative forms, as well as problems involving negative variables can always be rewritten into an equivalent problem in standard form.
Hope you like the above example of Linear Programming.Please leave your comments, if you have any doubts.
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