Q. Solve the following LPP by using graphical method
Maximize Z = x1+x2
Subject to constraints :
x1+x2≤
x1+x2≤
and x1,x2≥0.
Answer :
Graphical Method :
Convert the inequality constraints as equalities
x1+x2= - (1)
x1+x2= - (2)
Put x1= 0 in (1) => x2=
Let A = (0, )
Again put x2=0 in (1)=>x1=
Let B = ( ,0)
Put x2= 0 in (2) => x1=
Let C = ( ,0)
Put x1= 0 in (2) => x2=
Let D = (0, )
Using the above four points, construct graph
Let 'E' be the point of intersection of (1) and (2).
So, solve (1) and (2)
the values of units x1,x2 is
Therefore E = (, )
In the above graph, the feasible region is given by OAEC.
The values of Z at these vertices are given by
Vertex
Value of Z=x1+x2
O(0,0)
Z=0
A(0,)
Z=(0)+()=
E(,)
Z=()+()=
C(,0)
Z=()+(0)=
Therefore, The problem is of maximization type,the optimum solution
of the given problem is: Maximize Z = ,x1=and x2=