8. The tableau below is the initial tableau for a maximising linear programming problem.
| \(x\) | \(y\) | \(z\) | \(r\) | \(s\) | Value |
| \(r\) | 2 | 3 | 4 | 1 | 0 | 8 |
| \(s\) | 3 | 3 | 1 | 0 | 1 | 10 |
| \(P\) | - 8 | - 9 | - 5 | 0 | 0 | 0 |
- For this problem \(x \geq 0 , y \geq 0 , z \geq 0\). Write down the other two inequalities and the objective function.
- Solve this linear programming problem.
You may not need to use all of these tableaux.
| b.v. | \(x\) | \(y\) | \(z\) | \(r\) | \(s\) | Value |
| | | | | | |
| \(P\) | | | | | | |
| b.v. | \(x\) | \(y\) | \(z\) | \(r\) | \(s\) | Value |
| | | | | | |
| \(P\) | | | | | | |
| b.v. | \(x\) | \(y\) | \(z\) | \(r\) | \(s\) | Value |
| | | | | | |
| \(P\) | | | | | | |
| b.v. | \(x\) | \(y\) | \(z\) | \(r\) | \(s\) | Value |
| | | | | | |
| \(P\) | | | | | | |
- State the final value of \(P\), the objective function, and of each of the variables.