8. The tableau below is the initial tableau for a maximising linear programming problem in \(x , y\) and \(z\).
| Basic variable | \(x\) | \(y\) | \(z\) | \(r\) | \(S\) | \(t\) | Value |
| \(r\) | 4 | \(\frac { 7 } { 3 }\) | \(\frac { 5 } { 2 }\) | 1 | 0 | 0 | 64 |
| \(s\) | 1 | 3 | 0 | 0 | 1 | 0 | 16 |
| \(t\) | 4 | 2 | 2 | 0 | 0 | 1 | 60 |
| \(P\) | -5 | \(- \frac { 7 } { 2 }\) | -4 | 0 | 0 | 0 | 0 |
- Taking the most negative number in the profit row to indicate the pivot column at each stage, perform two complete iterations of the simplex algorithm. State the row operations you use. You may not need to use all of these tableaux.
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