5. In solving a three-variable maximising linear programming problem, the following tableau was obtained after the first iteration.
| Basic variable | \(x\) | \(y\) | \(z\) | \(r\) | \(s\) | \(t\) | Value |
| \(r\) | - 1 | 2 | 0 | 1 | 0 | 1 | 8 |
| \(s\) | - 1 | 3 | 0 | 0 | 1 | 1 | 22 |
| \(z\) | - 2 | 1 | 1 | 0 | 0 | 1 | 11 |
| \(P\) | 2 | - 5 | 0 | 0 | 0 | \(\frac { 1 } { 2 }\) | 15 |
- State which variable was increased first, giving a reason for your answer.
- Solve this linear programming problem. Make your method clear by stating the row operations you use.
- State the final value of the objective function and the final values of each variable.