6. The tableau below is the initial tableau for a maximising linear programming problem.
| Basic variable | \(x\) | \(y\) | \(z\) | \(r\) | \(s\) | \(t\) | Value |
| \(r\) | 16 | 2 | 4 | 1 | 0 | 0 | 350 |
| \(s\) | 18 | - 2 | 6 | 0 | 1 | 0 | 480 |
| \(t\) | 5 | 0 | 5 | 0 | 0 | 1 | 360 |
| \(P\) | - 18 | - 7 | - 20 | 0 | 0 | 0 | 0 |
- Write down the four equations represented in the initial tableau.
- 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 that you use.
- State whether or not your last tableau is optimal. Give a reason for your answer.