Graphical Method Example

Q1.Solve the following  LPP. This is an example for unbounded solution.

Maximize z = 3x1+2x2
subjected to  x1-x2 <= 1
                    x1+x2 >= 3
and x1,x2 >=0

Soln:                    

STEP I:
Let x1-x2 =1 --(1)
      x1+x2 =3 --(2)

(1) x1- x2 =1             (2) x1+ x2=3
Put x1=0                    Put x1=0
[x2 = -1] (0,-1)            [x2=3] (0,3)
Put x2=0                    Put x2=0
[x1=1] (1,0)                [x1=3] (3,0)

(1) (1,-1)                     (2) (3,3)

STEP II:

The solution space is unbounded. The maximum value of z occurs at infinity. Hence the problem has unbounded solution.


Q3. Max z=x1+x2
Subjected to x1+x2 <=1
-3x1 + x2 >=3
and x1, x2>=0.

This problem will provide a solution where there will be no common point and hence the feasible region cant be decided.