Simplex method to solve linear programming problem objective function maxz = 6X1 + 4x2 constraint condition: 2x1 + 3x2

Simplex method to solve linear programming problem objective function maxz = 6X1 + 4x2 constraint condition: 2x1 + 3x2

First, standardization:
Add relaxation variables X3, X4 (in order to make you see more regular, add a coefficient of 1,0): 1
max:z = 6 x1 + 4 x2
subject to:2 x1 + 3 x2 + 1 x3 + 0 x4 = 100
4 x1 + 2 x2 + 0 x3 + 1 x4 = 120
x1,x2,x3,x4>=0
The results show that the simplex augmented matrix is: 1, - 6, - 4,0,0,0
0,2,3,1,0,100
0,4,2,0,1,120
Then the matrix operation is carried out, which is reduced to 1,0,0,1 / 2,5 / 4200
0,1,0,-1/4,3/8,20
0,0,1,1/2,-1/4,20
(because this problem is very simple, the first three columns and three rows of the matrix can be directly transformed into the identity matrix, without any basic solution, test number, in base and out base. Please refer to the textbook for the specific principle.)
Then get the minimum value: 200, X1 = 20, X2 = 20 (the last column of the matrix)

max Z=2X1+4X2-5X3 X1+X2+X3=7 2X1-3X2+X3≥10 X1.X2.X3≥0

max Z=2X1+4X2-5X3
X1+X2+X3=7
X1.X2.X3≥0
x3=0
2X1-3X2≥10
X1+X2=7
max Z=2X1+4X2
x1=20/3 x2=1/3
max Z=40/3+4/3
=44/3

On the standardization of operations research
To standard type:
min f=|x|+|y|
s.t
x+2y>=10
x

0,5
-x3
+x4
Adding two unknowns becomes an equal sign