Question

Application of simplex method in operation research

Answer 1

Let us define an LP model as being in standard form if it satisfies the following two conditions:

All the constraints with the exception of the non-negativity restrictions are equations with non-negative right hand side. All the variables are non-negative.

For example,

Maximize z = 5 x 1 + 4 x 2 {\displaystyle z=5x_{1}+4x_{2}} subject to, 6 x 1 + 4 x 2 + s 1 = 24 {\displaystyle 6x_{1}+4x_{2}+s_{1}=24} , x 1 + 2 x 2 + s 2 = 6 {\displaystyle x_{1}+2x_{2}+s_{2}=6} , x 2 − x 1 + s 3 = 1 {\displaystyle x_{2}-x_{1}+s_{3}=1} , x 2 + s 4 = 2 {\displaystyle x_{2}+s_{4}=2} , x 1 , x 2 , s 1 , s 2 , s 3 , s 4 ≥ 0 {\displaystyle x_{1},x_{2},s_{1},s_{2},s_{3},s_{4}\geq 0}