LINEAR PROGRAMMING PROBLEM

                                 

              LINEAR PROGRAMMING PROBLEM

Linear Programming Problems are two types1. Maximization Problems such as Maximizing the Profit.

2. Minimization Problems such as minimizing the Cost.

The General form of an L.P.P is as follows:

Maximize or minimize Z = C1x1+ C2x2 + C3x3+……..+ Cnxn …………..(1)

Subject to the constraints

a11x1+a12x2+a13x3+………+a1nxn  or = or  b1

a21x1+a22x2+a23x3+……….+a2nxn or = or b2

………………………………………………… ………………….(2)

…………………………………………………

…………………………………………………

am1x1+am2x2+am3x3+……….+amnxn or = or bm

and x1, x2, x3…………..xn  0………………………………………….(3).                Objective Function

The equation Maximize or minimize Z = C1x1+ C2x2 + C3x3+……..+ Cnxn is called the 

Objective function.                             Constraints

The m inequalities

a11x1+a12x2+a13x3+………+a1nxn  or = or  b1

a21x1+a22x2+a23x3+……….+a2nxn or = or b2

………………………………………………… 

…………………………………………………

…………………………………………………

am1x1+am2x2+am3x3+……….+amnxn or = or bm

are called the constraint.                                Non-Negative Restriction

The n inequalities x1, x2, x3…………..xn  0 are called the Non-Negative Restriction.        Solution

Any vector (x1, x2, x3…………..xn) of real number which satisfies the constraints of an 

L.P.P is called a Solution of the L.P.P.

Feasible Solution

Any Solution of an L.P.P Which satisfies the non- negative restrictions also is called a 

feasible solution of the L.P.P.                  Optimal Solution

Any feasible solution of an L.P.P which optimizes (maximizes or minimizes as desired) 

the objective function is called the optimum solution of the L.P.P

infinite solution

An L.P.P may or may not have an optimum solution. Further, the optimum solution may 

be unique or infinite solution.

                                Thank you

T.GOPISANKAR             

I B.COM 

23UCM010

10.02.2024