Question

To use the dual simplex method to solve the following LPP :

Minimise z=x₁+2x₂+3x₃

subject to

x₁-x₂+x₃>= 4

x₁+x₂+2x₃<= 8

x₁-x₃ >= 2

x₁,x₂, x₃>= 0

Answer 1

Given inequality are-

x₁-x₂+x₃ $\ge$ 4

x₁+x₂+2x₃$\le$ 8

x₁-x₃ $\ge$ 2

x₁,x₂, x₃ $>$ 0

The Z-function is-

z=x₁+2x₂+3x₃

On solving The given inequality by eliminating $x_2$ from eqn.(1) and (2) and simultaneously solving the equation with eqs.(3)

and we found the critical point i.e. (3.6,1.2,1.6)

The value of Z is equla to $3.6+2(1.2)+3(1.6)=3.6+2.4+4.8=10.8$

Hence The minimum value is 10.8