Simplex Algorithm - Convert the LP problem to a system of linear equations.

Maximize p = x + 2y + 3z subject to the constraints

The initial tableau  is:


The final tableau is


The x-column is not cleared, so x = 0.
Since the y-column is cleared with pivot 3, the value of y is 6/3 = 2.
Since the z-column is cleared with pivot 1, the value of z is 6/1 = 6.
Since the t-column is cleared with pivot 3, the value of t is 48/3 = 16.
Since the s and u-columns are not cleared, their value is 0.
Since the p-column is cleared with pivot 3, the value of y is 66/3 = 22.


The constraints

in the above LP problem are written as equations by adding a new "slack" variable to the left-hand side of each to "take up the slack." In addition, the objective function is rewritten with all the unknowns on the left-hand side.

 -2x + 3y - 4z + p = 0 

This gives the following system of equations.

the initial tableau is as follows (notice how we separate the last row using a line).


Thus, the matrix containing all information has 4 rows and 8 columns.
Now enter edit matrix A under F7 using n=#rows=4 and m=#columns=8 .

         MATRIX A will look as follows:


The Solution is

x=0  ( as x column is not cleared)
y=7/4 = 1.75
z=33/2 =  16.5
p=111/4 = 27.75