4. A linear programming problem in \(x , y\) and \(z\) is described as follows. Maximise \(\quad P = - x + y\)
subject to $$\begin{gathered} x + 2 y + z \leqslant 15
3 x - 4 y + 2 z \geqslant 1
2 x + y + z = 14
x \geqslant 0 , y \geqslant 0 , z \geqslant 0 \end{gathered}$$

1. 1. Eliminate \(z\) from the first two inequality constraints, simplifying your answers.
   2. Hence state the maximum possible value of \(P\) Given that \(P\) takes the maximum possible value found in (a)(ii),
2. 1. determine the maximum possible value of \(x\)
   2. Hence find a solution to the linear programming problem.