Question

Minimize  

C = x − 8y + z

subject to  

x	−	2y	+	3z		≤		20
2x	+	y	−	2z		≤		30
2x	+	y	+	3z		≤		40
x ≥ 0, y ≥ 0, z ≥ 0

Answer 1

solution:

Using simplex method

Minimize C = x -8y + z subject to
x -2y + 3z <= 20
2x + y - 2z <= 20
2x + y +3z <= 40
x ≥ 0, y ≥ 0, z ≥ 0

Tableau #1
x y z s1 s2 s3 -c
1 -2 3 1 0 0 0 20   
2 1 -2 0 1 0 0 20   
2 1 3 0 0 1 0 40   
1 -8 1 0 0 0 1 0

Tableau #2
x y z s1 s2 s3 -c
5 0 -1 1 2 0 0 60   
2 1 -2 0 1 0 0 20   
0 0 5 0 -1 1 0 20   
17 0 -15 0 8 0 1 160

Tableau #3
x y z s1 s2 s3 -c
5 0 0 1 1.8 0.2 0 64   
2 1 0 0 0.6 0.4 0 28   
0 0 1 0 -0.2 0.2 0 4
17 0 0 0 5 3 1 220

Optimal Solution:

C = -220;

x = 0, y = 28, z = 4

Answer: C is minimize at x = 0 , y =28 and z =4 and its minimum value = -220