The term ‛programming′ means planning and it refers to a particular plan of action amongst several alternatives for maximizing profit or minimizing cost etc. Programming problems deal with determining optimal allocation of limited resources to meet the given objectives, such as cost, maximum profit, highest margin or least time, when resources have alternative uses.

The term ‛linear’ means that all inequations or equations used and the function to be maximized or minimized are linear. That is why linear programming deals with that class of problems for which all relations among the variables involved are linear.

Formally, linear programming deals with the optimization (maximization or minimization) of a linear function of a number of variables subject to a ¹equations in variables involved.

The general form of a linear programming problem is

Optimize (Maximize or Minimize) Z = c1x1 + c2x2 + ……..+ cnxn Subject to

a11 x1 + a12x2 + ….. + a1n xn (≤ , = , ≥) b1

a21 x1+ a22x2+ ….. + a2nxn (≤ , = , ≥ ) b2

. . . .

am1 x1+ am2 x2 + … + amn xn {≤ , = , ≥ { bmC

x1, x2….., xn ≥ 0

OBJECTIVE FUNCTION:

IF C1, C2.., Cn are constants and X1,X2,…..,Xn are variables, then the linear function Z = C1X1 + C2X2 + … + CnXn which is to be maximized or minimized is called the objective function. The objective function describes the primary purpose of the formulation of a linear programming problem and it is always non- negative. In business applications, the profit function which is to be maximized or the cost function which is to be minimized is called objective function.

CONSTRAINTS:

The inequations or equations in the variable of a LPP which describe the conditions under which the...

...Q.1. What is a linearprogramming problem ? Discuss the steps and role of linearprogramming is solving management problems. Discuss and describe the role of liner programming in managerial decision-making bringing out limitations, if any.
Ans : LinearProgramming is a mathematical technique useful for allocation of scarce or limited resources to several competing activities on the basis of...

...RESEARCH PAPER ON
LINEARPROGRAMMING
Vikas Vasam
ID: 100-11-5919
Faculty: Prof. Dr Goran Trajkovski
CMP 561: Algorithm Analysis
VIRGINIA INTERNATIONAL UNIVERSITY
Introduction:
One of the section of mathematical programming is linearprogramming.
Methods and linearprogramming models are widely used in the...

... LINEARPROGRAMMING
DATE;
5 JUNE, 14
UNIVERSITY OF CENTRAL PUNJAB
INTRODUCTION TO LINEARPROGRAMMINGLinearprogramming (LP; also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by...

...1. Discuss why and how you would use a liner programming model for a project of your choice, either from your own work or as a hypothetical situation. Be sure that you stae your situation first, before you develpp the LP model
Linearprogramming is a modeling technique that is used to help managers make logical and informed decisions. All date and input factors are known with certainty. Linear program models are developed in...

...LinearProgramming is a mathematical technique useful for allocation of scarce or limited resources to several competing activities on the basis of given criterion of optimality.The usefulness of linearprogramming as a tool for optimal decision-making on resource allocation, is based on its applicability to many diversified decision problems. The effective use and application requires, as on its applicability to many diversified...

...Z00_REND1011_11_SE_MOD7 PP2.QXD
2/21/11
12:39 PM
Page 1
7
MODULE
LinearProgramming:
The Simplex Method
LEARNING OBJECTIVES
After completing this chapter, students will be able to:
1. Convert LP constraints to equalities with slack,
surplus, and artificial variables.
2. Set up and solve LP problems with simplex tableaus.
3. Interpret the meaning of every number in a simplex
tableau.
4. Recognize special cases such as infeasibility,...

...LinearProgramming Concept Paper
There are two types of linearprogramming:
1. LinearProgramming- involves no more than 2 variables, linearprogramming problems can be structured to minimize costs as well as maximize profits. Due to the increasing complexity of business organizations, the role of the management executive as a decision maker is becoming more and more difficult....

...SMEToolKit.org
[pic]Linearprogramming is very important in various fields of life especially in managerial decision making. The reason is that it helps the company in minimizing the costs and maximizing the profits. Through linearprogramming managers can calculate the prices and the sales units which can maximize the profits of the company. Therefore, there are various issues which the company incurs regarding their costs and prices...