Display the following linear programming problem in a Simplex tableau.
Maximise \(\quad P = 4 x + 3 y + z\)
subject to
$$\begin{aligned}
& 2 x + y + z \leqslant 25
& x + 2 y + z \leqslant 40
& x + y + 2 z \leqslant 30
\end{aligned}$$
and \(x \geqslant 0 , \quad y \geqslant 0 , \quad z \geqslant 0\).
The first pivot to be chosen is from the \(x\)-column.
Perform one iteration of the Simplex method.
Perform one further iteration.
Interpret your final tableau and state the values of your slack variables.