Linear Programming Problem(LPP)
An equation with same degree/variable/power is a Ist order equation.
LP model has few basic elements which are described below.
Decision Variable - The variable whose values determine the solution of a problem.
Objective function - the generalized format of an objective function is given as
maximize or minimize z =c1x1+c2x2 +.........+cnxn
where c1,c2,...cn are cost variables and x1,x2 ...xn are decision variables.
Technical Coefficient : (aij)
aij is the amount of resource i required for the activity j where i varies from 1 to m and j varies from 1 to n.
The generalized format of technical coefficient is
[ a11 a12 .....a1n
a21 a22 .....a2n
.
.
am1 am2 ... amn ]
Resource Availability: (bi)
The constant bi is the amount of resource i available during the planning period.
The general format is given as,
[b1
b2
.
.
bm]
Set of Constraints:
A
constraint is a kind of restriction on the total amount of a particular
resource required to carry out activities atvarious levels.
The generalized format is given as:
a11x1+a12x2+...+a1nxn <=,= or >= b1
a21x1+a22x2+...+a2nxn <=, = or >= b2
.
.
am1x1+am2x2+...+amnxn<= ,= or >=bm
Non negativity constraint:
Each and every decision variable in LP model is a non negative variable.
The general format is
x1,x2..xn >=0
Mathematical formulation of LPP:
The general format is given by
Maximize/Minimize z = c1x1+c2x2+...+cnxn --- (1 )
subjected to constraints
a11x1+a12x2+...+a1nxn <=,= or >= b1
a21x1+a22x2+...+a2nxn <=,= or >= b2
. ---(2)
.
an1xn+anx2+...+amnxn<= , = or >=bm
and x1,x2,...xn >=0 ---(3)
variables are involved .
Definition of LPP :
Linear
Programming problem deals with optimization of functions of decision
variables known as objective functions subject to a set of simultaneous
linear eqution known as constraints.
Applications:
LP technique is used in many indusrial and economic problems , airlines , railways, food processing etc.,
