Use the dual simplex method to solve the following LP minimz

Use the dual simplex method to solve the following LP.

minimze z= 3x1+2x2+3
s.t

3x1+x2+x33
-3x1+3x2+x26
x1+x2+x33

Solution

minimze z= 3x1+2x2+3
s.t

3x1+x2+x33
-3x1+3x2+x36
x1+x2+x33

I equation + II equation give

4x2+2x3>=9

Also x2+x3 >= 3-3x1 >= 3-(6-3x2-x3)

i.e. x2+x3 >= -3+3x2+x3

-2x2>=-3

Or x2 <= 1.5

x3>=1.5

Hence corner points are (0, 1.5,1.5) (-1, 0, 3) and (-1,3,0)

Values of z are

i) 6

ii) 0

iii) 9

Hence optimal solution is (x1,x2,x3) = (-1, 0, 3)