Homework Answers
| Iteration-1 | Cj | 90 | 70 | 60 | 50 | 0 | 0 | 0 | ||
| B | CB | XB | x1 | x2 | x3 | x4 | S1 | S2 | S3 | MinRatio |
| XBx1 | ||||||||||
| S1 | 0 | 490 | 0 | 0 | 0.375 | 0.625 | 1 | 0 | 0 | --- |
| S2 | 0 | 570 | 0 | 0.75 | 0.5 | 0.375 | 0 | 1 | 0 | --- |
| S3 | 0 | 300 | -1 | 0.25 | 0.125 | 0 | 0 | 0 | 1 | 300/1=300→ |
| Z=0 | Zj | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||
| Zj-Cj | -90↑ | -70 | -60 | -50 | 0 | 0 | 0 |
Negative minimum Zj-Cj is -90 and its column index is 1. So, the entering variable is x1.
Minimum ratio is 300 and its row index is 3. So, the leaving basis variable is S3.
∴ The pivot element is 1.
Entering =x1, Departing =S3, Key Element =1
| Iteration-2 | Cj | 90 | 70 | 60 | 50 | 0 | 0 | 0 | ||
| B | CB | XB | x1 | x2 | x3 | x4 | S1 | S2 | S3 | MinRatio |
| XBx4 | ||||||||||
| S1 | 0 | 490 | 0 | 0 | 0.375 | -0.625 | 1 | 0 | 0 | 490/0.625=784→ |
| S2 | 0 | 570 | 0 | 0.75 | 0.5 | 0.375 | 0 | 1 | 0 | 570/0.375=1520 |
| x1 | 90 | 300 | 1 | 0.25 | 0.125 | 0 | 0 | 0 | 1 | --- |
| Z=27000 | Zj | 90 | 22.5 | 11.25 | 0 | 0 | 0 | 90 | ||
| Zj-Cj | 0 | -47.5 | -48.75 | -50↑ | 0 | 0 | 90 |
Negative minimum Zj-Cj is -50 and its column index is 4. So, the entering variable is x4.
Minimum ratio is 784 and its row index is 1. So, the leaving basis variable is S1.
∴ The pivot element is 0.625.
Entering =x4, Departing =S1, Key Element =0.625
| Iteration-3 | Cj | 90 | 70 | 60 | 50 | 0 | 0 | 0 | ||
| B | CB | XB | x1 | x2 | x3 | x4 | S1 | S2 | S3 | MinRatio |
| XBx2 | ||||||||||
| x4 | 50 | 784 | 0 | 0 | 0.6 | 1 | 1.6 | 0 | 0 | --- |
| S2 | 0 | 276 | 0 | -0.75 | 0.275 | 0 | -0.6 | 1 | 0 | 276/0.75=368→ |
| x1 | 90 | 300 | 1 | 0.25 | 0.125 | 0 | 0 | 0 | 1 | 300/0.25=1200 |
| Z=66200 | Zj | 90 | 22.5 | 41.25 | 50 | 80 | 0 | 90 | ||
| Zj-Cj | 0 | -47.5↑ | -18.75 | 0 | 80 | 0 | 90 |
Negative minimum Zj-Cj is -47.5 and its column index is 2. So, the entering variable is x2.
Minimum ratio is 368 and its row index is 2. So, the leaving basis variable is S2.
∴ The pivot element is 0.75.
Entering =x2, Departing =S2, Key Element =0.75
| Iteration-4 | Cj | 90 | 70 | 60 | 50 | 0 | 0 | 0 | ||
| B | CB | XB | x1 | x2 | x3 | x4 | S1 | S2 | S3 | MinRatio |
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