8. A three-variable linear programming problem in \(x , y\) and \(z\) is to be solved. The objective is to maximise the profit P . The following tableau was obtained.
| Basic variable | \(x\) | \(y\) | \(Z\) | \(r\) | \(s\) | \(t\) | Value |
| S | 3 | 0 | 2 | 0 | 1 | \(- \frac { 2 } { 3 }\) | \(\frac { 2 } { 3 }\) |
| \(r\) | 4 | 0 | \(\frac { 7 } { 2 }\) | 1 | 0 | 8 | \(\frac { 9 } { 2 }\) |
| \(y\) | 5 | 1 | 7 | 0 | 0 | 3 | 7 |
| P | 3 | 0 | 2 | 0 | 0 | 8 | 63 |
- State, giving your reason, whether this tableau represents the optimal solution.
- State the values of every variable.
- Calculate the profit made on each unit of \(y\).