GRAPHICAL METHOD
Graph 5x+2y=180 and 3x+2y=135.
Lines intersect at 2x=45, x=22.5, 2y=135-3x=135-67.5=67.5, y=33.75.
Since x,y≥0 we have a triangle ABC with vertices A(22.5,33.75), B(36,0), C(45,0).
Z=300x+200y for each point:
ZA=13500; ZB=10800; Zc=13500. So max Z is achieved for A or C using this method.
SIMPLEX METHOD
TABLEAUX
ROW |
x |
y |
s1 |
s2 |
Z |
Result |
Ratio |
Op/Comment |
R1 |
5✔️ |
2 |
1 |
0 |
0 |
180 |
36 |
Pivot row |
R2 |
3 |
2 |
0 |
1 |
0 |
135 |
45 |
|
R3 |
-300 |
-200 |
0 |
0 |
1 |
|
|
Objective |
R1 |
1 |
0.4 |
0.2 |
0 |
0 |
36 |
|
R1/5
(adjust pivot row) |
R2 |
3 |
2 |
0 |
1 |
0 |
135 |
|
|
R3 |
-300 |
-200 |
0 |
0 |
1 |
0 |
|
|
R1 |
1 |
0.4 |
0.2 |
0 |
0 |
36 |
90 |
|
R2 |
0 |
0.8✔️ |
-0.6 |
1 |
0 |
27 |
33.75 |
R2-3R1
(next pivot row) |
R3 |
0 |
-80 |
60 |
0 |
1 |
10800 |
|
R3+300R1 |
R1 |
1 |
0.4 |
0.2 |
0 |
0 |
36 |
|
|
R2 |
0 |
1 |
-0.75 |
1.25 |
0 |
33.75 |
|
R2/0.8
(adjust pivot row) |
R3 |
0 |
-80 |
60 |
0 |
1 |
10800 |
|
|
R1 |
1 |
0 |
0.5 |
-0.5 |
0 |
22.5 |
|
R1-0.4R2 |
R2 |
0 |
1 |
-0.75 |
1.25 |
0 |
33.75 |
|
|
R3 |
0 |
0 |
0 |
100 |
1 |
13500 |
|
R3+80R2 (finish) |
See following comment.